Is the percentage symbol a constant?












14












$begingroup$


Isn't the percentage symbol actually just a constant with the value $0.01$? As in
$$
15% = 15 times % = 15 times 0.01 = 0.15
$$

I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?










share|cite|improve this question









New contributor




Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$








  • 5




    $begingroup$
    Right, you can very well see $%$ as a numerical constant, though culturally this would shock many people.
    $endgroup$
    – Yves Daoust
    16 hours ago






  • 1




    $begingroup$
    It is not a unit of measure; it is only a useful symbol. 15% is $dfrac {15}{100}$. A percentage is a number.
    $endgroup$
    – Mauro ALLEGRANZA
    16 hours ago








  • 3




    $begingroup$
    I agree completely that % can be considered a real number.
    $endgroup$
    – JP McCarthy
    16 hours ago










  • $begingroup$
    As the others said. I would though recommend avoiding writing $15times %$ as it is unusual and may confuse people.
    $endgroup$
    – Taladris
    14 hours ago






  • 1




    $begingroup$
    Some believe that it's a map $Bbb R to Bbb R^*$ that assigns to $x$ the functional $x%(y)=frac{xy}{100}$. Not that they know it, but they rather perceive it. And it becomes apparent when they describe their difficulties.
    $endgroup$
    – Saucy O'Path
    11 hours ago


















14












$begingroup$


Isn't the percentage symbol actually just a constant with the value $0.01$? As in
$$
15% = 15 times % = 15 times 0.01 = 0.15
$$

I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?










share|cite|improve this question









New contributor




Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$








  • 5




    $begingroup$
    Right, you can very well see $%$ as a numerical constant, though culturally this would shock many people.
    $endgroup$
    – Yves Daoust
    16 hours ago






  • 1




    $begingroup$
    It is not a unit of measure; it is only a useful symbol. 15% is $dfrac {15}{100}$. A percentage is a number.
    $endgroup$
    – Mauro ALLEGRANZA
    16 hours ago








  • 3




    $begingroup$
    I agree completely that % can be considered a real number.
    $endgroup$
    – JP McCarthy
    16 hours ago










  • $begingroup$
    As the others said. I would though recommend avoiding writing $15times %$ as it is unusual and may confuse people.
    $endgroup$
    – Taladris
    14 hours ago






  • 1




    $begingroup$
    Some believe that it's a map $Bbb R to Bbb R^*$ that assigns to $x$ the functional $x%(y)=frac{xy}{100}$. Not that they know it, but they rather perceive it. And it becomes apparent when they describe their difficulties.
    $endgroup$
    – Saucy O'Path
    11 hours ago
















14












14








14


1



$begingroup$


Isn't the percentage symbol actually just a constant with the value $0.01$? As in
$$
15% = 15 times % = 15 times 0.01 = 0.15
$$

I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?










share|cite|improve this question









New contributor




Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.







$endgroup$




Isn't the percentage symbol actually just a constant with the value $0.01$? As in
$$
15% = 15 times % = 15 times 0.01 = 0.15
$$

I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?







notation percentages unit-of-measure






share|cite|improve this question









New contributor




Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.











share|cite|improve this question









New contributor




Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









share|cite|improve this question




share|cite|improve this question








edited 11 hours ago









Pedro

10.6k23173




10.6k23173






New contributor




Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.









asked 16 hours ago









Rudolph GottesheimRudolph Gottesheim

1745




1745




New contributor




Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.





New contributor





Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






Rudolph Gottesheim is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.








  • 5




    $begingroup$
    Right, you can very well see $%$ as a numerical constant, though culturally this would shock many people.
    $endgroup$
    – Yves Daoust
    16 hours ago






  • 1




    $begingroup$
    It is not a unit of measure; it is only a useful symbol. 15% is $dfrac {15}{100}$. A percentage is a number.
    $endgroup$
    – Mauro ALLEGRANZA
    16 hours ago








  • 3




    $begingroup$
    I agree completely that % can be considered a real number.
    $endgroup$
    – JP McCarthy
    16 hours ago










  • $begingroup$
    As the others said. I would though recommend avoiding writing $15times %$ as it is unusual and may confuse people.
    $endgroup$
    – Taladris
    14 hours ago






  • 1




    $begingroup$
    Some believe that it's a map $Bbb R to Bbb R^*$ that assigns to $x$ the functional $x%(y)=frac{xy}{100}$. Not that they know it, but they rather perceive it. And it becomes apparent when they describe their difficulties.
    $endgroup$
    – Saucy O'Path
    11 hours ago
















  • 5




    $begingroup$
    Right, you can very well see $%$ as a numerical constant, though culturally this would shock many people.
    $endgroup$
    – Yves Daoust
    16 hours ago






  • 1




    $begingroup$
    It is not a unit of measure; it is only a useful symbol. 15% is $dfrac {15}{100}$. A percentage is a number.
    $endgroup$
    – Mauro ALLEGRANZA
    16 hours ago








  • 3




    $begingroup$
    I agree completely that % can be considered a real number.
    $endgroup$
    – JP McCarthy
    16 hours ago










  • $begingroup$
    As the others said. I would though recommend avoiding writing $15times %$ as it is unusual and may confuse people.
    $endgroup$
    – Taladris
    14 hours ago






  • 1




    $begingroup$
    Some believe that it's a map $Bbb R to Bbb R^*$ that assigns to $x$ the functional $x%(y)=frac{xy}{100}$. Not that they know it, but they rather perceive it. And it becomes apparent when they describe their difficulties.
    $endgroup$
    – Saucy O'Path
    11 hours ago










5




5




$begingroup$
Right, you can very well see $%$ as a numerical constant, though culturally this would shock many people.
$endgroup$
– Yves Daoust
16 hours ago




$begingroup$
Right, you can very well see $%$ as a numerical constant, though culturally this would shock many people.
$endgroup$
– Yves Daoust
16 hours ago




1




1




$begingroup$
It is not a unit of measure; it is only a useful symbol. 15% is $dfrac {15}{100}$. A percentage is a number.
$endgroup$
– Mauro ALLEGRANZA
16 hours ago






$begingroup$
It is not a unit of measure; it is only a useful symbol. 15% is $dfrac {15}{100}$. A percentage is a number.
$endgroup$
– Mauro ALLEGRANZA
16 hours ago






3




3




$begingroup$
I agree completely that % can be considered a real number.
$endgroup$
– JP McCarthy
16 hours ago




$begingroup$
I agree completely that % can be considered a real number.
$endgroup$
– JP McCarthy
16 hours ago












$begingroup$
As the others said. I would though recommend avoiding writing $15times %$ as it is unusual and may confuse people.
$endgroup$
– Taladris
14 hours ago




$begingroup$
As the others said. I would though recommend avoiding writing $15times %$ as it is unusual and may confuse people.
$endgroup$
– Taladris
14 hours ago




1




1




$begingroup$
Some believe that it's a map $Bbb R to Bbb R^*$ that assigns to $x$ the functional $x%(y)=frac{xy}{100}$. Not that they know it, but they rather perceive it. And it becomes apparent when they describe their difficulties.
$endgroup$
– Saucy O'Path
11 hours ago






$begingroup$
Some believe that it's a map $Bbb R to Bbb R^*$ that assigns to $x$ the functional $x%(y)=frac{xy}{100}$. Not that they know it, but they rather perceive it. And it becomes apparent when they describe their difficulties.
$endgroup$
– Saucy O'Path
11 hours ago












12 Answers
12






active

oldest

votes


















8












$begingroup$

There are some exceptions. Take for example $20 + 50%$. This is often interpreted to be equal to $30$, while $20 + 50 cdot 0.01 = 20.5$.



There is some discussion about whether $20 + 50%$ is a valid notation. But sometimes it is used and Google and Wolfram Alpha interpret it as $20cdot 1.5$.



I'm also thinking about $50%^2$. I don't think you'll see this notation (and you shouldn't use it), but just as a thought experiment: Is this $0.25$ or $0.005$?






share|cite|improve this answer











$endgroup$









  • 4




    $begingroup$
    But the convention that $20+50%=30$ leads to bizarre results such as $20 + 50% - 50% = 15$ or $20 + 100% - 100% = 0$.
    $endgroup$
    – gandalf61
    14 hours ago








  • 6




    $begingroup$
    20 + 50% does not mean anything per se. Seeing the 20 as 100% is understandable, but not guaranteed. +50% does not instantly imply *150% as gandalf61 illustrated.
    $endgroup$
    – Chieron
    14 hours ago






  • 2




    $begingroup$
    @gandalf61 I agree with you. But the notation $x+y%$ is not uncommon when weights of products, tolerance of resistors, density of chemical solutions, etc. are reported. If you worry about the algebra, then the algebra is not associative which is true about many other mathematical objects as well. I think this is a very good answer. (+1).
    $endgroup$
    – stressed out
    13 hours ago








  • 1




    $begingroup$
    AFAIK, many pocket calculators use this convention as well.
    $endgroup$
    – Sebastian Reichelt
    13 hours ago






  • 3




    $begingroup$
    My point is that the $+$ sign in this convention is not addition. It is shorthand for a different operator $oplus$ which can be defined as $a oplus b = a times (1+b)$. With this interpretation $20 oplus 50% = 20 times (1+50%) = 20 times (1+50 times 0.01) = 20 times 1.5 = 30$ and we are good.
    $endgroup$
    – gandalf61
    13 hours ago





















7












$begingroup$

Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.






share|cite|improve this answer









$endgroup$









  • 3




    $begingroup$
    % means "per hundred", which makes it an operation, not a constant. The OP is correct except for "15 x %".
    $endgroup$
    – amI
    12 hours ago



















5












$begingroup$

I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".



So
$$
5% = 5 (text{multiply by} frac{1}{100})=frac{5}{100}=0,05
$$

in the same way as
$$
2 text{kilograms}=2 (text{multiply by $1000$})text{ grams}= 2000 text{grams}
$$



I usually teach my students this way and I found it to work just fine.






share|cite











$endgroup$









  • 2




    $begingroup$
    Um... the $-$ prefix ($-x$/$-1x$/$x-2x$) sounds better to me as a prefix example, LOL. Also, $!$ is a good postfix example (if we disregard the double, triple, etc. factorials). :P
    $endgroup$
    – EKons
    12 hours ago





















4












$begingroup$


Isn't the percentage symbol actually just a constant with the value $0.01$?




No. If it were, all of the following would be valid constructs:



$$
30+%50=30.5\
90%cm=0.9cm\
2-%=1.99\
%^2=0.0001
$$



The percentage symbol is a unit. When converting between units, it's easy to treat them as constants that represent the conversion ratio, and multiply (for example, the $m$ unit can be thought of as a constant equal to $10cm$, in $2m=2(10cm)=20cm$). But that isn't the same as saying they're "just constants", as they represent more than that. A unit is not just a ratio, it's a distance or a weight or an amount of time.



This is less obvious with $%$ because it's a dimensionless unit, representing something more abstract like "parts of a whole" rather than a physical property like mass or surface area. $1%$ is "one one-hundredth of a thing", measuring an amount of something, anything, often something with its own units. A similarly dimensionless unit is the "degree", where $1^circ$ is "one three-hundred-sixtieth of the way around". Another one is the "cycle", as in "one $Mhz$ is one million cycles per second". Things like "wholes", "turns", and "cycles" are more abstract than inches or grams, but when applied they still represent tangible measurements, so they aren't any less powerful when treated as units.






I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?




What then would you say the "constant" is that is represented by "inch", or "second", or "ounce"? Would these ideas not have clear numeric values if every unit were simply a constant?



Again, a unit is not just a constant, it represents something more. I don't have exact vocabulary for this, but I would say a unit is an "amount" of a "dimension". The dimension can be time, space, energy, mass, etc. To even begin to treat a unit as a constant, we need to consider it in terms of a different unit in the same dimension. For example, the unit "millisecond" amounts to different constants depending on whether we think about it in terms of a second ($0.001$), hour ($2.77778times10^{-7}$), microsecond ($1000$), etc. This constant is not intrinsic to the units themselves, as it only arises when comparing to other unit systems.






share|cite|improve this answer








New contributor




DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
Check out our Code of Conduct.






$endgroup$





















    3












    $begingroup$

    Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.



    However, it is agreed around the world that you should not write something like "$250%$ liters of water".



    So it is a good idea to think of it as a constant, but not write it as a constant.



    Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.






    share|cite|improve this answer











    $endgroup$













    • $begingroup$
      I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
      $endgroup$
      – Yves Daoust
      16 hours ago












    • $begingroup$
      @YvesDaoust: Aside from what seems to be typo, I don't see anything wrong with that usage. If I wanted to translate the equation 5% * 15 EUR = 75% EUR into words, I'd say "five percent of fifteen euros is seventy-five percent of a euro," which sounds fine to me. Similarly, I'd read 5% * 20 EUR = 100% EUR as "five percent of twenty euros is one hundred percent of a euro—that is, one whole euro."
      $endgroup$
      – Vectornaut
      13 hours ago










    • $begingroup$
      @Vectornaut: no typo.
      $endgroup$
      – Yves Daoust
      13 hours ago










    • $begingroup$
      @YvesDaoust: If there's no typo, I'm having trouble understanding what you wrote. Do we agree that 5%$ = 5% * $1 = 0.05 * $1 = $0.05?
      $endgroup$
      – Vectornaut
      12 hours ago












    • $begingroup$
      Wait a minute—the MathJax processor was doing funny things to the dollar signs in my last post until I escaped them. Maybe your initial post is displaying differently for me than for you?
      $endgroup$
      – Vectornaut
      12 hours ago



















    2












    $begingroup$

    The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.






    share|cite|improve this answer









    $endgroup$





















      2












      $begingroup$

      If you want to think about units or dimensional analysis, then probably it is best to interpret 15% as



      $$ 15% = frac{text{$15$ units of X}}{text{$100$ units of X}} $$



      (I would read this as "15 units of X per 100 units of X".) For example, the Wikipedia page on dimensional analysis gives the example of debt-to-GDP ratio.
      $$ 90% text{ debt-to-GDP} = frac{text{$90$ dollars of debt}}{text{per $100$ dollars of GDP}} $$



      Here both the top and bottom are dollars. But they are two different dollar measurements. So even though the percentage is a dimensionless quantity (dollars/dollars), keeping the units in mind may be wise. Similarly



      $$ 10% text{ full} = frac{text{$10$ liters of water}}{text{per $100$ liters of container}} . $$



      and so on. (edit) So for example, if you want to do a calculation like "How many liters of water are in a 2-gallon container that is 10% full", you do



      $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$3.78$ liters of container}}{text{$1$ gallon of container}} ~ cdot ~ frac{text{$10$ liters of water}}{text{$100$ liters of container}} . $$



      Of course you could have also done



      $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$10$ gallons of water}}{text{$100$ gallons of container}} ~ cdot ~ frac{text{$3.78$ liters of water}}{text{$1$ gallon of water}} ~ cdot . $$






      share|cite|improve this answer











      $endgroup$





















        0












        $begingroup$

        I believe you can think of it both ways.



        It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.






        share|cite|improve this answer









        $endgroup$





















          0












          $begingroup$

          I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.



          In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.






          share|cite|improve this answer









          $endgroup$





















            0












            $begingroup$

            It is not a constant. It can be thought of as a unit if you like, but is probably best thought of as merely a syntax. A phrasing I find effective is to say that they are different spellings of a number.



            The reason it is not a constant is because it cannot be used in all situations where a constant could be used. For example, $100x$ cannot be meaningfully written as $frac{x}{%}$. Were $%$ to be a constant, that would be a reasonable thing to write. It would be as reasonable as writing $frac{x}{pi}$.



            You can get away with thinking of percents as units. Like with your approach of treating it as a constant, the math tends to work out. However, it doesn't really work well as a unit in general. While the axiomization of units is still an open problem, it is typically not true that $100 m = 1 frac{m}{%}$ or $1 m = 100 mcdot %$. This makes it an awkward sort of unit.



            I do see "%" used as a unit from time to time, but it's typically shorthand for a particular percentage. I might see a graph of a chemical reaction efficiency written as "%/mol". Indeed, this is using "%" as a unit, but in such a graph it would really be a shorthand for "percent efficiency of the reaction." The same graph might instead be labeled with "%yield/mol" without really changing the meaning any. In this case, I think it is clear that "%" is not really acting as a unit in the way you might be used to. It's really just a letter, no different than "a" or "q."



            Instead, perhaps the most reliable way of treating percents is as an alternate spelling for a number when writing it down. This is a nuanced difference: it suggests that 10% and 0.1 are not just equal, they are in fact merely two ways of writing down the same number. This would be no different than how a programmer might write 0x1F to denote the number 31 in a base-16 notation, how a Chinese person might elect to write 三十一 to denote the same number, or how we might write "thirty one." They are merely different ways of writing the same number.



            This is a subtle difference, but sometimes it can be helpful. For example, at some point you will come across the proof that 0.9999.... = 1.0. This proof is very disconcerting at first, because you assume 0.9999... and 1.0 are two distinct numbers, so they could never be equal. But when you really dig into the meaning of that funny little "..." symbol, you discover there's a better way to think of it. "0.9999..." and "1.0" are simply two spellings of the same number. One relies on an infinite series to acquire its meaning, while the other does not, but they mean the same number.






            share|cite|improve this answer









            $endgroup$





















              0












              $begingroup$

              It is just a notation i.e. a way of expressing numbers, e.g.



              $0.01 = 1% =10^{-2} = 1text{e-}02$



              nothing more. This is also why it is said to be dimensionless.



              There is absolutely nothing wrong in saying that someone is $20$ or $2000%$ years old, unusual admittedly.






              share|cite|improve this answer











              $endgroup$





















                0












                $begingroup$

                It's often convenient to write $x%$ for $x/100$. The notation $xy$ is also used for the product of $x$ and $y$ (whether numbers, functions, elements of a group, etc.), and these give the same result if you formally set $% = 1/100$. On the other hand, it would be bizarre to write "$1/%$ is divisible by $5$" or "$% + sqrt{%} = 0.11$", etc. There's nothing inherently wrong with abusing notation; I have no problem writing $0$ for the integer $0$, the real number $0$, the zero function, the zero element in a vector space, etc. But there's also nothing particularly noteworthy or profound in doing so.






                share|cite|improve this answer









                $endgroup$













                  Your Answer





                  StackExchange.ifUsing("editor", function () {
                  return StackExchange.using("mathjaxEditing", function () {
                  StackExchange.MarkdownEditor.creationCallbacks.add(function (editor, postfix) {
                  StackExchange.mathjaxEditing.prepareWmdForMathJax(editor, postfix, [["$", "$"], ["\\(","\\)"]]);
                  });
                  });
                  }, "mathjax-editing");

                  StackExchange.ready(function() {
                  var channelOptions = {
                  tags: "".split(" "),
                  id: "69"
                  };
                  initTagRenderer("".split(" "), "".split(" "), channelOptions);

                  StackExchange.using("externalEditor", function() {
                  // Have to fire editor after snippets, if snippets enabled
                  if (StackExchange.settings.snippets.snippetsEnabled) {
                  StackExchange.using("snippets", function() {
                  createEditor();
                  });
                  }
                  else {
                  createEditor();
                  }
                  });

                  function createEditor() {
                  StackExchange.prepareEditor({
                  heartbeatType: 'answer',
                  autoActivateHeartbeat: false,
                  convertImagesToLinks: true,
                  noModals: true,
                  showLowRepImageUploadWarning: true,
                  reputationToPostImages: 10,
                  bindNavPrevention: true,
                  postfix: "",
                  imageUploader: {
                  brandingHtml: "Powered by u003ca class="icon-imgur-white" href="https://imgur.com/"u003eu003c/au003e",
                  contentPolicyHtml: "User contributions licensed under u003ca href="https://creativecommons.org/licenses/by-sa/3.0/"u003ecc by-sa 3.0 with attribution requiredu003c/au003e u003ca href="https://stackoverflow.com/legal/content-policy"u003e(content policy)u003c/au003e",
                  allowUrls: true
                  },
                  noCode: true, onDemand: true,
                  discardSelector: ".discard-answer"
                  ,immediatelyShowMarkdownHelp:true
                  });


                  }
                  });






                  Rudolph Gottesheim is a new contributor. Be nice, and check out our Code of Conduct.










                  draft saved

                  draft discarded


















                  StackExchange.ready(
                  function () {
                  StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3122554%2fis-the-percentage-symbol-a-constant%23new-answer', 'question_page');
                  }
                  );

                  Post as a guest















                  Required, but never shown

























                  12 Answers
                  12






                  active

                  oldest

                  votes








                  12 Answers
                  12






                  active

                  oldest

                  votes









                  active

                  oldest

                  votes






                  active

                  oldest

                  votes









                  8












                  $begingroup$

                  There are some exceptions. Take for example $20 + 50%$. This is often interpreted to be equal to $30$, while $20 + 50 cdot 0.01 = 20.5$.



                  There is some discussion about whether $20 + 50%$ is a valid notation. But sometimes it is used and Google and Wolfram Alpha interpret it as $20cdot 1.5$.



                  I'm also thinking about $50%^2$. I don't think you'll see this notation (and you shouldn't use it), but just as a thought experiment: Is this $0.25$ or $0.005$?






                  share|cite|improve this answer











                  $endgroup$









                  • 4




                    $begingroup$
                    But the convention that $20+50%=30$ leads to bizarre results such as $20 + 50% - 50% = 15$ or $20 + 100% - 100% = 0$.
                    $endgroup$
                    – gandalf61
                    14 hours ago








                  • 6




                    $begingroup$
                    20 + 50% does not mean anything per se. Seeing the 20 as 100% is understandable, but not guaranteed. +50% does not instantly imply *150% as gandalf61 illustrated.
                    $endgroup$
                    – Chieron
                    14 hours ago






                  • 2




                    $begingroup$
                    @gandalf61 I agree with you. But the notation $x+y%$ is not uncommon when weights of products, tolerance of resistors, density of chemical solutions, etc. are reported. If you worry about the algebra, then the algebra is not associative which is true about many other mathematical objects as well. I think this is a very good answer. (+1).
                    $endgroup$
                    – stressed out
                    13 hours ago








                  • 1




                    $begingroup$
                    AFAIK, many pocket calculators use this convention as well.
                    $endgroup$
                    – Sebastian Reichelt
                    13 hours ago






                  • 3




                    $begingroup$
                    My point is that the $+$ sign in this convention is not addition. It is shorthand for a different operator $oplus$ which can be defined as $a oplus b = a times (1+b)$. With this interpretation $20 oplus 50% = 20 times (1+50%) = 20 times (1+50 times 0.01) = 20 times 1.5 = 30$ and we are good.
                    $endgroup$
                    – gandalf61
                    13 hours ago


















                  8












                  $begingroup$

                  There are some exceptions. Take for example $20 + 50%$. This is often interpreted to be equal to $30$, while $20 + 50 cdot 0.01 = 20.5$.



                  There is some discussion about whether $20 + 50%$ is a valid notation. But sometimes it is used and Google and Wolfram Alpha interpret it as $20cdot 1.5$.



                  I'm also thinking about $50%^2$. I don't think you'll see this notation (and you shouldn't use it), but just as a thought experiment: Is this $0.25$ or $0.005$?






                  share|cite|improve this answer











                  $endgroup$









                  • 4




                    $begingroup$
                    But the convention that $20+50%=30$ leads to bizarre results such as $20 + 50% - 50% = 15$ or $20 + 100% - 100% = 0$.
                    $endgroup$
                    – gandalf61
                    14 hours ago








                  • 6




                    $begingroup$
                    20 + 50% does not mean anything per se. Seeing the 20 as 100% is understandable, but not guaranteed. +50% does not instantly imply *150% as gandalf61 illustrated.
                    $endgroup$
                    – Chieron
                    14 hours ago






                  • 2




                    $begingroup$
                    @gandalf61 I agree with you. But the notation $x+y%$ is not uncommon when weights of products, tolerance of resistors, density of chemical solutions, etc. are reported. If you worry about the algebra, then the algebra is not associative which is true about many other mathematical objects as well. I think this is a very good answer. (+1).
                    $endgroup$
                    – stressed out
                    13 hours ago








                  • 1




                    $begingroup$
                    AFAIK, many pocket calculators use this convention as well.
                    $endgroup$
                    – Sebastian Reichelt
                    13 hours ago






                  • 3




                    $begingroup$
                    My point is that the $+$ sign in this convention is not addition. It is shorthand for a different operator $oplus$ which can be defined as $a oplus b = a times (1+b)$. With this interpretation $20 oplus 50% = 20 times (1+50%) = 20 times (1+50 times 0.01) = 20 times 1.5 = 30$ and we are good.
                    $endgroup$
                    – gandalf61
                    13 hours ago
















                  8












                  8








                  8





                  $begingroup$

                  There are some exceptions. Take for example $20 + 50%$. This is often interpreted to be equal to $30$, while $20 + 50 cdot 0.01 = 20.5$.



                  There is some discussion about whether $20 + 50%$ is a valid notation. But sometimes it is used and Google and Wolfram Alpha interpret it as $20cdot 1.5$.



                  I'm also thinking about $50%^2$. I don't think you'll see this notation (and you shouldn't use it), but just as a thought experiment: Is this $0.25$ or $0.005$?






                  share|cite|improve this answer











                  $endgroup$



                  There are some exceptions. Take for example $20 + 50%$. This is often interpreted to be equal to $30$, while $20 + 50 cdot 0.01 = 20.5$.



                  There is some discussion about whether $20 + 50%$ is a valid notation. But sometimes it is used and Google and Wolfram Alpha interpret it as $20cdot 1.5$.



                  I'm also thinking about $50%^2$. I don't think you'll see this notation (and you shouldn't use it), but just as a thought experiment: Is this $0.25$ or $0.005$?







                  share|cite|improve this answer














                  share|cite|improve this answer



                  share|cite|improve this answer








                  edited 7 hours ago

























                  answered 14 hours ago









                  PaulPaul

                  1,746910




                  1,746910








                  • 4




                    $begingroup$
                    But the convention that $20+50%=30$ leads to bizarre results such as $20 + 50% - 50% = 15$ or $20 + 100% - 100% = 0$.
                    $endgroup$
                    – gandalf61
                    14 hours ago








                  • 6




                    $begingroup$
                    20 + 50% does not mean anything per se. Seeing the 20 as 100% is understandable, but not guaranteed. +50% does not instantly imply *150% as gandalf61 illustrated.
                    $endgroup$
                    – Chieron
                    14 hours ago






                  • 2




                    $begingroup$
                    @gandalf61 I agree with you. But the notation $x+y%$ is not uncommon when weights of products, tolerance of resistors, density of chemical solutions, etc. are reported. If you worry about the algebra, then the algebra is not associative which is true about many other mathematical objects as well. I think this is a very good answer. (+1).
                    $endgroup$
                    – stressed out
                    13 hours ago








                  • 1




                    $begingroup$
                    AFAIK, many pocket calculators use this convention as well.
                    $endgroup$
                    – Sebastian Reichelt
                    13 hours ago






                  • 3




                    $begingroup$
                    My point is that the $+$ sign in this convention is not addition. It is shorthand for a different operator $oplus$ which can be defined as $a oplus b = a times (1+b)$. With this interpretation $20 oplus 50% = 20 times (1+50%) = 20 times (1+50 times 0.01) = 20 times 1.5 = 30$ and we are good.
                    $endgroup$
                    – gandalf61
                    13 hours ago
















                  • 4




                    $begingroup$
                    But the convention that $20+50%=30$ leads to bizarre results such as $20 + 50% - 50% = 15$ or $20 + 100% - 100% = 0$.
                    $endgroup$
                    – gandalf61
                    14 hours ago








                  • 6




                    $begingroup$
                    20 + 50% does not mean anything per se. Seeing the 20 as 100% is understandable, but not guaranteed. +50% does not instantly imply *150% as gandalf61 illustrated.
                    $endgroup$
                    – Chieron
                    14 hours ago






                  • 2




                    $begingroup$
                    @gandalf61 I agree with you. But the notation $x+y%$ is not uncommon when weights of products, tolerance of resistors, density of chemical solutions, etc. are reported. If you worry about the algebra, then the algebra is not associative which is true about many other mathematical objects as well. I think this is a very good answer. (+1).
                    $endgroup$
                    – stressed out
                    13 hours ago








                  • 1




                    $begingroup$
                    AFAIK, many pocket calculators use this convention as well.
                    $endgroup$
                    – Sebastian Reichelt
                    13 hours ago






                  • 3




                    $begingroup$
                    My point is that the $+$ sign in this convention is not addition. It is shorthand for a different operator $oplus$ which can be defined as $a oplus b = a times (1+b)$. With this interpretation $20 oplus 50% = 20 times (1+50%) = 20 times (1+50 times 0.01) = 20 times 1.5 = 30$ and we are good.
                    $endgroup$
                    – gandalf61
                    13 hours ago










                  4




                  4




                  $begingroup$
                  But the convention that $20+50%=30$ leads to bizarre results such as $20 + 50% - 50% = 15$ or $20 + 100% - 100% = 0$.
                  $endgroup$
                  – gandalf61
                  14 hours ago






                  $begingroup$
                  But the convention that $20+50%=30$ leads to bizarre results such as $20 + 50% - 50% = 15$ or $20 + 100% - 100% = 0$.
                  $endgroup$
                  – gandalf61
                  14 hours ago






                  6




                  6




                  $begingroup$
                  20 + 50% does not mean anything per se. Seeing the 20 as 100% is understandable, but not guaranteed. +50% does not instantly imply *150% as gandalf61 illustrated.
                  $endgroup$
                  – Chieron
                  14 hours ago




                  $begingroup$
                  20 + 50% does not mean anything per se. Seeing the 20 as 100% is understandable, but not guaranteed. +50% does not instantly imply *150% as gandalf61 illustrated.
                  $endgroup$
                  – Chieron
                  14 hours ago




                  2




                  2




                  $begingroup$
                  @gandalf61 I agree with you. But the notation $x+y%$ is not uncommon when weights of products, tolerance of resistors, density of chemical solutions, etc. are reported. If you worry about the algebra, then the algebra is not associative which is true about many other mathematical objects as well. I think this is a very good answer. (+1).
                  $endgroup$
                  – stressed out
                  13 hours ago






                  $begingroup$
                  @gandalf61 I agree with you. But the notation $x+y%$ is not uncommon when weights of products, tolerance of resistors, density of chemical solutions, etc. are reported. If you worry about the algebra, then the algebra is not associative which is true about many other mathematical objects as well. I think this is a very good answer. (+1).
                  $endgroup$
                  – stressed out
                  13 hours ago






                  1




                  1




                  $begingroup$
                  AFAIK, many pocket calculators use this convention as well.
                  $endgroup$
                  – Sebastian Reichelt
                  13 hours ago




                  $begingroup$
                  AFAIK, many pocket calculators use this convention as well.
                  $endgroup$
                  – Sebastian Reichelt
                  13 hours ago




                  3




                  3




                  $begingroup$
                  My point is that the $+$ sign in this convention is not addition. It is shorthand for a different operator $oplus$ which can be defined as $a oplus b = a times (1+b)$. With this interpretation $20 oplus 50% = 20 times (1+50%) = 20 times (1+50 times 0.01) = 20 times 1.5 = 30$ and we are good.
                  $endgroup$
                  – gandalf61
                  13 hours ago






                  $begingroup$
                  My point is that the $+$ sign in this convention is not addition. It is shorthand for a different operator $oplus$ which can be defined as $a oplus b = a times (1+b)$. With this interpretation $20 oplus 50% = 20 times (1+50%) = 20 times (1+50 times 0.01) = 20 times 1.5 = 30$ and we are good.
                  $endgroup$
                  – gandalf61
                  13 hours ago













                  7












                  $begingroup$

                  Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.






                  share|cite|improve this answer









                  $endgroup$









                  • 3




                    $begingroup$
                    % means "per hundred", which makes it an operation, not a constant. The OP is correct except for "15 x %".
                    $endgroup$
                    – amI
                    12 hours ago
















                  7












                  $begingroup$

                  Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.






                  share|cite|improve this answer









                  $endgroup$









                  • 3




                    $begingroup$
                    % means "per hundred", which makes it an operation, not a constant. The OP is correct except for "15 x %".
                    $endgroup$
                    – amI
                    12 hours ago














                  7












                  7








                  7





                  $begingroup$

                  Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.






                  share|cite|improve this answer









                  $endgroup$



                  Yes, for calculations you can use $%=frac{1}{100}$. Of course what is meant by the symbol is an interpretation as "parts of hundred", i.e. as percentage of a given amount.







                  share|cite|improve this answer












                  share|cite|improve this answer



                  share|cite|improve this answer










                  answered 16 hours ago









                  JamesJames

                  1,557217




                  1,557217








                  • 3




                    $begingroup$
                    % means "per hundred", which makes it an operation, not a constant. The OP is correct except for "15 x %".
                    $endgroup$
                    – amI
                    12 hours ago














                  • 3




                    $begingroup$
                    % means "per hundred", which makes it an operation, not a constant. The OP is correct except for "15 x %".
                    $endgroup$
                    – amI
                    12 hours ago








                  3




                  3




                  $begingroup$
                  % means "per hundred", which makes it an operation, not a constant. The OP is correct except for "15 x %".
                  $endgroup$
                  – amI
                  12 hours ago




                  $begingroup$
                  % means "per hundred", which makes it an operation, not a constant. The OP is correct except for "15 x %".
                  $endgroup$
                  – amI
                  12 hours ago











                  5












                  $begingroup$

                  I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".



                  So
                  $$
                  5% = 5 (text{multiply by} frac{1}{100})=frac{5}{100}=0,05
                  $$

                  in the same way as
                  $$
                  2 text{kilograms}=2 (text{multiply by $1000$})text{ grams}= 2000 text{grams}
                  $$



                  I usually teach my students this way and I found it to work just fine.






                  share|cite











                  $endgroup$









                  • 2




                    $begingroup$
                    Um... the $-$ prefix ($-x$/$-1x$/$x-2x$) sounds better to me as a prefix example, LOL. Also, $!$ is a good postfix example (if we disregard the double, triple, etc. factorials). :P
                    $endgroup$
                    – EKons
                    12 hours ago


















                  5












                  $begingroup$

                  I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".



                  So
                  $$
                  5% = 5 (text{multiply by} frac{1}{100})=frac{5}{100}=0,05
                  $$

                  in the same way as
                  $$
                  2 text{kilograms}=2 (text{multiply by $1000$})text{ grams}= 2000 text{grams}
                  $$



                  I usually teach my students this way and I found it to work just fine.






                  share|cite











                  $endgroup$









                  • 2




                    $begingroup$
                    Um... the $-$ prefix ($-x$/$-1x$/$x-2x$) sounds better to me as a prefix example, LOL. Also, $!$ is a good postfix example (if we disregard the double, triple, etc. factorials). :P
                    $endgroup$
                    – EKons
                    12 hours ago
















                  5












                  5








                  5





                  $begingroup$

                  I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".



                  So
                  $$
                  5% = 5 (text{multiply by} frac{1}{100})=frac{5}{100}=0,05
                  $$

                  in the same way as
                  $$
                  2 text{kilograms}=2 (text{multiply by $1000$})text{ grams}= 2000 text{grams}
                  $$



                  I usually teach my students this way and I found it to work just fine.






                  share|cite











                  $endgroup$



                  I would´t say that $%$ has a value. You can think of $%$ as "multiply by $frac{1}{100}"$. As a sort of a postfix. In the same way as you can think of the "kilo-" prefix as "multiply by $1000$".



                  So
                  $$
                  5% = 5 (text{multiply by} frac{1}{100})=frac{5}{100}=0,05
                  $$

                  in the same way as
                  $$
                  2 text{kilograms}=2 (text{multiply by $1000$})text{ grams}= 2000 text{grams}
                  $$



                  I usually teach my students this way and I found it to work just fine.







                  share|cite














                  share|cite



                  share|cite








                  edited 7 hours ago

























                  answered 16 hours ago









                  Vinyl_coat_jawaVinyl_coat_jawa

                  2,7141029




                  2,7141029








                  • 2




                    $begingroup$
                    Um... the $-$ prefix ($-x$/$-1x$/$x-2x$) sounds better to me as a prefix example, LOL. Also, $!$ is a good postfix example (if we disregard the double, triple, etc. factorials). :P
                    $endgroup$
                    – EKons
                    12 hours ago
















                  • 2




                    $begingroup$
                    Um... the $-$ prefix ($-x$/$-1x$/$x-2x$) sounds better to me as a prefix example, LOL. Also, $!$ is a good postfix example (if we disregard the double, triple, etc. factorials). :P
                    $endgroup$
                    – EKons
                    12 hours ago










                  2




                  2




                  $begingroup$
                  Um... the $-$ prefix ($-x$/$-1x$/$x-2x$) sounds better to me as a prefix example, LOL. Also, $!$ is a good postfix example (if we disregard the double, triple, etc. factorials). :P
                  $endgroup$
                  – EKons
                  12 hours ago






                  $begingroup$
                  Um... the $-$ prefix ($-x$/$-1x$/$x-2x$) sounds better to me as a prefix example, LOL. Also, $!$ is a good postfix example (if we disregard the double, triple, etc. factorials). :P
                  $endgroup$
                  – EKons
                  12 hours ago













                  4












                  $begingroup$


                  Isn't the percentage symbol actually just a constant with the value $0.01$?




                  No. If it were, all of the following would be valid constructs:



                  $$
                  30+%50=30.5\
                  90%cm=0.9cm\
                  2-%=1.99\
                  %^2=0.0001
                  $$



                  The percentage symbol is a unit. When converting between units, it's easy to treat them as constants that represent the conversion ratio, and multiply (for example, the $m$ unit can be thought of as a constant equal to $10cm$, in $2m=2(10cm)=20cm$). But that isn't the same as saying they're "just constants", as they represent more than that. A unit is not just a ratio, it's a distance or a weight or an amount of time.



                  This is less obvious with $%$ because it's a dimensionless unit, representing something more abstract like "parts of a whole" rather than a physical property like mass or surface area. $1%$ is "one one-hundredth of a thing", measuring an amount of something, anything, often something with its own units. A similarly dimensionless unit is the "degree", where $1^circ$ is "one three-hundred-sixtieth of the way around". Another one is the "cycle", as in "one $Mhz$ is one million cycles per second". Things like "wholes", "turns", and "cycles" are more abstract than inches or grams, but when applied they still represent tangible measurements, so they aren't any less powerful when treated as units.






                  I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?




                  What then would you say the "constant" is that is represented by "inch", or "second", or "ounce"? Would these ideas not have clear numeric values if every unit were simply a constant?



                  Again, a unit is not just a constant, it represents something more. I don't have exact vocabulary for this, but I would say a unit is an "amount" of a "dimension". The dimension can be time, space, energy, mass, etc. To even begin to treat a unit as a constant, we need to consider it in terms of a different unit in the same dimension. For example, the unit "millisecond" amounts to different constants depending on whether we think about it in terms of a second ($0.001$), hour ($2.77778times10^{-7}$), microsecond ($1000$), etc. This constant is not intrinsic to the units themselves, as it only arises when comparing to other unit systems.






                  share|cite|improve this answer








                  New contributor




                  DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                  Check out our Code of Conduct.






                  $endgroup$


















                    4












                    $begingroup$


                    Isn't the percentage symbol actually just a constant with the value $0.01$?




                    No. If it were, all of the following would be valid constructs:



                    $$
                    30+%50=30.5\
                    90%cm=0.9cm\
                    2-%=1.99\
                    %^2=0.0001
                    $$



                    The percentage symbol is a unit. When converting between units, it's easy to treat them as constants that represent the conversion ratio, and multiply (for example, the $m$ unit can be thought of as a constant equal to $10cm$, in $2m=2(10cm)=20cm$). But that isn't the same as saying they're "just constants", as they represent more than that. A unit is not just a ratio, it's a distance or a weight or an amount of time.



                    This is less obvious with $%$ because it's a dimensionless unit, representing something more abstract like "parts of a whole" rather than a physical property like mass or surface area. $1%$ is "one one-hundredth of a thing", measuring an amount of something, anything, often something with its own units. A similarly dimensionless unit is the "degree", where $1^circ$ is "one three-hundred-sixtieth of the way around". Another one is the "cycle", as in "one $Mhz$ is one million cycles per second". Things like "wholes", "turns", and "cycles" are more abstract than inches or grams, but when applied they still represent tangible measurements, so they aren't any less powerful when treated as units.






                    I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?




                    What then would you say the "constant" is that is represented by "inch", or "second", or "ounce"? Would these ideas not have clear numeric values if every unit were simply a constant?



                    Again, a unit is not just a constant, it represents something more. I don't have exact vocabulary for this, but I would say a unit is an "amount" of a "dimension". The dimension can be time, space, energy, mass, etc. To even begin to treat a unit as a constant, we need to consider it in terms of a different unit in the same dimension. For example, the unit "millisecond" amounts to different constants depending on whether we think about it in terms of a second ($0.001$), hour ($2.77778times10^{-7}$), microsecond ($1000$), etc. This constant is not intrinsic to the units themselves, as it only arises when comparing to other unit systems.






                    share|cite|improve this answer








                    New contributor




                    DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                    Check out our Code of Conduct.






                    $endgroup$
















                      4












                      4








                      4





                      $begingroup$


                      Isn't the percentage symbol actually just a constant with the value $0.01$?




                      No. If it were, all of the following would be valid constructs:



                      $$
                      30+%50=30.5\
                      90%cm=0.9cm\
                      2-%=1.99\
                      %^2=0.0001
                      $$



                      The percentage symbol is a unit. When converting between units, it's easy to treat them as constants that represent the conversion ratio, and multiply (for example, the $m$ unit can be thought of as a constant equal to $10cm$, in $2m=2(10cm)=20cm$). But that isn't the same as saying they're "just constants", as they represent more than that. A unit is not just a ratio, it's a distance or a weight or an amount of time.



                      This is less obvious with $%$ because it's a dimensionless unit, representing something more abstract like "parts of a whole" rather than a physical property like mass or surface area. $1%$ is "one one-hundredth of a thing", measuring an amount of something, anything, often something with its own units. A similarly dimensionless unit is the "degree", where $1^circ$ is "one three-hundred-sixtieth of the way around". Another one is the "cycle", as in "one $Mhz$ is one million cycles per second". Things like "wholes", "turns", and "cycles" are more abstract than inches or grams, but when applied they still represent tangible measurements, so they aren't any less powerful when treated as units.






                      I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?




                      What then would you say the "constant" is that is represented by "inch", or "second", or "ounce"? Would these ideas not have clear numeric values if every unit were simply a constant?



                      Again, a unit is not just a constant, it represents something more. I don't have exact vocabulary for this, but I would say a unit is an "amount" of a "dimension". The dimension can be time, space, energy, mass, etc. To even begin to treat a unit as a constant, we need to consider it in terms of a different unit in the same dimension. For example, the unit "millisecond" amounts to different constants depending on whether we think about it in terms of a second ($0.001$), hour ($2.77778times10^{-7}$), microsecond ($1000$), etc. This constant is not intrinsic to the units themselves, as it only arises when comparing to other unit systems.






                      share|cite|improve this answer








                      New contributor




                      DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.






                      $endgroup$




                      Isn't the percentage symbol actually just a constant with the value $0.01$?




                      No. If it were, all of the following would be valid constructs:



                      $$
                      30+%50=30.5\
                      90%cm=0.9cm\
                      2-%=1.99\
                      %^2=0.0001
                      $$



                      The percentage symbol is a unit. When converting between units, it's easy to treat them as constants that represent the conversion ratio, and multiply (for example, the $m$ unit can be thought of as a constant equal to $10cm$, in $2m=2(10cm)=20cm$). But that isn't the same as saying they're "just constants", as they represent more than that. A unit is not just a ratio, it's a distance or a weight or an amount of time.



                      This is less obvious with $%$ because it's a dimensionless unit, representing something more abstract like "parts of a whole" rather than a physical property like mass or surface area. $1%$ is "one one-hundredth of a thing", measuring an amount of something, anything, often something with its own units. A similarly dimensionless unit is the "degree", where $1^circ$ is "one three-hundred-sixtieth of the way around". Another one is the "cycle", as in "one $Mhz$ is one million cycles per second". Things like "wholes", "turns", and "cycles" are more abstract than inches or grams, but when applied they still represent tangible measurements, so they aren't any less powerful when treated as units.






                      I mean, I guess every unit is actually just a constant, but why do we treat them in such a special way then?




                      What then would you say the "constant" is that is represented by "inch", or "second", or "ounce"? Would these ideas not have clear numeric values if every unit were simply a constant?



                      Again, a unit is not just a constant, it represents something more. I don't have exact vocabulary for this, but I would say a unit is an "amount" of a "dimension". The dimension can be time, space, energy, mass, etc. To even begin to treat a unit as a constant, we need to consider it in terms of a different unit in the same dimension. For example, the unit "millisecond" amounts to different constants depending on whether we think about it in terms of a second ($0.001$), hour ($2.77778times10^{-7}$), microsecond ($1000$), etc. This constant is not intrinsic to the units themselves, as it only arises when comparing to other unit systems.







                      share|cite|improve this answer








                      New contributor




                      DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.









                      share|cite|improve this answer



                      share|cite|improve this answer






                      New contributor




                      DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.









                      answered 7 hours ago









                      DarthFennecDarthFennec

                      1411




                      1411




                      New contributor




                      DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.





                      New contributor





                      DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.






                      DarthFennec is a new contributor to this site. Take care in asking for clarification, commenting, and answering.
                      Check out our Code of Conduct.























                          3












                          $begingroup$

                          Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.



                          However, it is agreed around the world that you should not write something like "$250%$ liters of water".



                          So it is a good idea to think of it as a constant, but not write it as a constant.



                          Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.






                          share|cite|improve this answer











                          $endgroup$













                          • $begingroup$
                            I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
                            $endgroup$
                            – Yves Daoust
                            16 hours ago












                          • $begingroup$
                            @YvesDaoust: Aside from what seems to be typo, I don't see anything wrong with that usage. If I wanted to translate the equation 5% * 15 EUR = 75% EUR into words, I'd say "five percent of fifteen euros is seventy-five percent of a euro," which sounds fine to me. Similarly, I'd read 5% * 20 EUR = 100% EUR as "five percent of twenty euros is one hundred percent of a euro—that is, one whole euro."
                            $endgroup$
                            – Vectornaut
                            13 hours ago










                          • $begingroup$
                            @Vectornaut: no typo.
                            $endgroup$
                            – Yves Daoust
                            13 hours ago










                          • $begingroup$
                            @YvesDaoust: If there's no typo, I'm having trouble understanding what you wrote. Do we agree that 5%$ = 5% * $1 = 0.05 * $1 = $0.05?
                            $endgroup$
                            – Vectornaut
                            12 hours ago












                          • $begingroup$
                            Wait a minute—the MathJax processor was doing funny things to the dollar signs in my last post until I escaped them. Maybe your initial post is displaying differently for me than for you?
                            $endgroup$
                            – Vectornaut
                            12 hours ago
















                          3












                          $begingroup$

                          Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.



                          However, it is agreed around the world that you should not write something like "$250%$ liters of water".



                          So it is a good idea to think of it as a constant, but not write it as a constant.



                          Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.






                          share|cite|improve this answer











                          $endgroup$













                          • $begingroup$
                            I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
                            $endgroup$
                            – Yves Daoust
                            16 hours ago












                          • $begingroup$
                            @YvesDaoust: Aside from what seems to be typo, I don't see anything wrong with that usage. If I wanted to translate the equation 5% * 15 EUR = 75% EUR into words, I'd say "five percent of fifteen euros is seventy-five percent of a euro," which sounds fine to me. Similarly, I'd read 5% * 20 EUR = 100% EUR as "five percent of twenty euros is one hundred percent of a euro—that is, one whole euro."
                            $endgroup$
                            – Vectornaut
                            13 hours ago










                          • $begingroup$
                            @Vectornaut: no typo.
                            $endgroup$
                            – Yves Daoust
                            13 hours ago










                          • $begingroup$
                            @YvesDaoust: If there's no typo, I'm having trouble understanding what you wrote. Do we agree that 5%$ = 5% * $1 = 0.05 * $1 = $0.05?
                            $endgroup$
                            – Vectornaut
                            12 hours ago












                          • $begingroup$
                            Wait a minute—the MathJax processor was doing funny things to the dollar signs in my last post until I escaped them. Maybe your initial post is displaying differently for me than for you?
                            $endgroup$
                            – Vectornaut
                            12 hours ago














                          3












                          3








                          3





                          $begingroup$

                          Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.



                          However, it is agreed around the world that you should not write something like "$250%$ liters of water".



                          So it is a good idea to think of it as a constant, but not write it as a constant.



                          Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.






                          share|cite|improve this answer











                          $endgroup$



                          Well, it really depends. In Chinese schools, students are told that $100%=1,40%=2/5$, so % is a constant. In the UK examination system, it appears that % is treated as a unit. Students are NOT expected to write the above two expressions.



                          However, it is agreed around the world that you should not write something like "$250%$ liters of water".



                          So it is a good idea to think of it as a constant, but not write it as a constant.



                          Other units like cm, mm, kg are like the basis of a vector space or something or the imaginary unit $i^2=1$. The are NOT even like usual numbers because they cannot be added together.







                          share|cite|improve this answer














                          share|cite|improve this answer



                          share|cite|improve this answer








                          edited 16 hours ago









                          J. W. Tanner

                          2,3751117




                          2,3751117










                          answered 16 hours ago









                          Holding ArthurHolding Arthur

                          1,014417




                          1,014417












                          • $begingroup$
                            I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
                            $endgroup$
                            – Yves Daoust
                            16 hours ago












                          • $begingroup$
                            @YvesDaoust: Aside from what seems to be typo, I don't see anything wrong with that usage. If I wanted to translate the equation 5% * 15 EUR = 75% EUR into words, I'd say "five percent of fifteen euros is seventy-five percent of a euro," which sounds fine to me. Similarly, I'd read 5% * 20 EUR = 100% EUR as "five percent of twenty euros is one hundred percent of a euro—that is, one whole euro."
                            $endgroup$
                            – Vectornaut
                            13 hours ago










                          • $begingroup$
                            @Vectornaut: no typo.
                            $endgroup$
                            – Yves Daoust
                            13 hours ago










                          • $begingroup$
                            @YvesDaoust: If there's no typo, I'm having trouble understanding what you wrote. Do we agree that 5%$ = 5% * $1 = 0.05 * $1 = $0.05?
                            $endgroup$
                            – Vectornaut
                            12 hours ago












                          • $begingroup$
                            Wait a minute—the MathJax processor was doing funny things to the dollar signs in my last post until I escaped them. Maybe your initial post is displaying differently for me than for you?
                            $endgroup$
                            – Vectornaut
                            12 hours ago


















                          • $begingroup$
                            I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
                            $endgroup$
                            – Yves Daoust
                            16 hours ago












                          • $begingroup$
                            @YvesDaoust: Aside from what seems to be typo, I don't see anything wrong with that usage. If I wanted to translate the equation 5% * 15 EUR = 75% EUR into words, I'd say "five percent of fifteen euros is seventy-five percent of a euro," which sounds fine to me. Similarly, I'd read 5% * 20 EUR = 100% EUR as "five percent of twenty euros is one hundred percent of a euro—that is, one whole euro."
                            $endgroup$
                            – Vectornaut
                            13 hours ago










                          • $begingroup$
                            @Vectornaut: no typo.
                            $endgroup$
                            – Yves Daoust
                            13 hours ago










                          • $begingroup$
                            @YvesDaoust: If there's no typo, I'm having trouble understanding what you wrote. Do we agree that 5%$ = 5% * $1 = 0.05 * $1 = $0.05?
                            $endgroup$
                            – Vectornaut
                            12 hours ago












                          • $begingroup$
                            Wait a minute—the MathJax processor was doing funny things to the dollar signs in my last post until I escaped them. Maybe your initial post is displaying differently for me than for you?
                            $endgroup$
                            – Vectornaut
                            12 hours ago
















                          $begingroup$
                          I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
                          $endgroup$
                          – Yves Daoust
                          16 hours ago






                          $begingroup$
                          I also leads to incongruities like $5%$ of two hundred Dollars is $5%$$ ?!
                          $endgroup$
                          – Yves Daoust
                          16 hours ago














                          $begingroup$
                          @YvesDaoust: Aside from what seems to be typo, I don't see anything wrong with that usage. If I wanted to translate the equation 5% * 15 EUR = 75% EUR into words, I'd say "five percent of fifteen euros is seventy-five percent of a euro," which sounds fine to me. Similarly, I'd read 5% * 20 EUR = 100% EUR as "five percent of twenty euros is one hundred percent of a euro—that is, one whole euro."
                          $endgroup$
                          – Vectornaut
                          13 hours ago




                          $begingroup$
                          @YvesDaoust: Aside from what seems to be typo, I don't see anything wrong with that usage. If I wanted to translate the equation 5% * 15 EUR = 75% EUR into words, I'd say "five percent of fifteen euros is seventy-five percent of a euro," which sounds fine to me. Similarly, I'd read 5% * 20 EUR = 100% EUR as "five percent of twenty euros is one hundred percent of a euro—that is, one whole euro."
                          $endgroup$
                          – Vectornaut
                          13 hours ago












                          $begingroup$
                          @Vectornaut: no typo.
                          $endgroup$
                          – Yves Daoust
                          13 hours ago




                          $begingroup$
                          @Vectornaut: no typo.
                          $endgroup$
                          – Yves Daoust
                          13 hours ago












                          $begingroup$
                          @YvesDaoust: If there's no typo, I'm having trouble understanding what you wrote. Do we agree that 5%$ = 5% * $1 = 0.05 * $1 = $0.05?
                          $endgroup$
                          – Vectornaut
                          12 hours ago






                          $begingroup$
                          @YvesDaoust: If there's no typo, I'm having trouble understanding what you wrote. Do we agree that 5%$ = 5% * $1 = 0.05 * $1 = $0.05?
                          $endgroup$
                          – Vectornaut
                          12 hours ago














                          $begingroup$
                          Wait a minute—the MathJax processor was doing funny things to the dollar signs in my last post until I escaped them. Maybe your initial post is displaying differently for me than for you?
                          $endgroup$
                          – Vectornaut
                          12 hours ago




                          $begingroup$
                          Wait a minute—the MathJax processor was doing funny things to the dollar signs in my last post until I escaped them. Maybe your initial post is displaying differently for me than for you?
                          $endgroup$
                          – Vectornaut
                          12 hours ago











                          2












                          $begingroup$

                          The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.






                          share|cite|improve this answer









                          $endgroup$


















                            2












                            $begingroup$

                            The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.






                            share|cite|improve this answer









                            $endgroup$
















                              2












                              2








                              2





                              $begingroup$

                              The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.






                              share|cite|improve this answer









                              $endgroup$



                              The percent sign is an abbreviation: just substitute "$color{red}%$" by "${}color{red}{cdotfrac{1}{100}}$", that's all. So for example: $15color{red}{%}=15color{red}{cdotfrac{1}{100}}=0.15$. Or the other way round: $1.23=123color{red}{cdotfrac{1}{100}}=123color{red}{%}$.







                              share|cite|improve this answer












                              share|cite|improve this answer



                              share|cite|improve this answer










                              answered 15 hours ago









                              Michael HoppeMichael Hoppe

                              11.1k31836




                              11.1k31836























                                  2












                                  $begingroup$

                                  If you want to think about units or dimensional analysis, then probably it is best to interpret 15% as



                                  $$ 15% = frac{text{$15$ units of X}}{text{$100$ units of X}} $$



                                  (I would read this as "15 units of X per 100 units of X".) For example, the Wikipedia page on dimensional analysis gives the example of debt-to-GDP ratio.
                                  $$ 90% text{ debt-to-GDP} = frac{text{$90$ dollars of debt}}{text{per $100$ dollars of GDP}} $$



                                  Here both the top and bottom are dollars. But they are two different dollar measurements. So even though the percentage is a dimensionless quantity (dollars/dollars), keeping the units in mind may be wise. Similarly



                                  $$ 10% text{ full} = frac{text{$10$ liters of water}}{text{per $100$ liters of container}} . $$



                                  and so on. (edit) So for example, if you want to do a calculation like "How many liters of water are in a 2-gallon container that is 10% full", you do



                                  $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$3.78$ liters of container}}{text{$1$ gallon of container}} ~ cdot ~ frac{text{$10$ liters of water}}{text{$100$ liters of container}} . $$



                                  Of course you could have also done



                                  $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$10$ gallons of water}}{text{$100$ gallons of container}} ~ cdot ~ frac{text{$3.78$ liters of water}}{text{$1$ gallon of water}} ~ cdot . $$






                                  share|cite|improve this answer











                                  $endgroup$


















                                    2












                                    $begingroup$

                                    If you want to think about units or dimensional analysis, then probably it is best to interpret 15% as



                                    $$ 15% = frac{text{$15$ units of X}}{text{$100$ units of X}} $$



                                    (I would read this as "15 units of X per 100 units of X".) For example, the Wikipedia page on dimensional analysis gives the example of debt-to-GDP ratio.
                                    $$ 90% text{ debt-to-GDP} = frac{text{$90$ dollars of debt}}{text{per $100$ dollars of GDP}} $$



                                    Here both the top and bottom are dollars. But they are two different dollar measurements. So even though the percentage is a dimensionless quantity (dollars/dollars), keeping the units in mind may be wise. Similarly



                                    $$ 10% text{ full} = frac{text{$10$ liters of water}}{text{per $100$ liters of container}} . $$



                                    and so on. (edit) So for example, if you want to do a calculation like "How many liters of water are in a 2-gallon container that is 10% full", you do



                                    $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$3.78$ liters of container}}{text{$1$ gallon of container}} ~ cdot ~ frac{text{$10$ liters of water}}{text{$100$ liters of container}} . $$



                                    Of course you could have also done



                                    $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$10$ gallons of water}}{text{$100$ gallons of container}} ~ cdot ~ frac{text{$3.78$ liters of water}}{text{$1$ gallon of water}} ~ cdot . $$






                                    share|cite|improve this answer











                                    $endgroup$
















                                      2












                                      2








                                      2





                                      $begingroup$

                                      If you want to think about units or dimensional analysis, then probably it is best to interpret 15% as



                                      $$ 15% = frac{text{$15$ units of X}}{text{$100$ units of X}} $$



                                      (I would read this as "15 units of X per 100 units of X".) For example, the Wikipedia page on dimensional analysis gives the example of debt-to-GDP ratio.
                                      $$ 90% text{ debt-to-GDP} = frac{text{$90$ dollars of debt}}{text{per $100$ dollars of GDP}} $$



                                      Here both the top and bottom are dollars. But they are two different dollar measurements. So even though the percentage is a dimensionless quantity (dollars/dollars), keeping the units in mind may be wise. Similarly



                                      $$ 10% text{ full} = frac{text{$10$ liters of water}}{text{per $100$ liters of container}} . $$



                                      and so on. (edit) So for example, if you want to do a calculation like "How many liters of water are in a 2-gallon container that is 10% full", you do



                                      $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$3.78$ liters of container}}{text{$1$ gallon of container}} ~ cdot ~ frac{text{$10$ liters of water}}{text{$100$ liters of container}} . $$



                                      Of course you could have also done



                                      $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$10$ gallons of water}}{text{$100$ gallons of container}} ~ cdot ~ frac{text{$3.78$ liters of water}}{text{$1$ gallon of water}} ~ cdot . $$






                                      share|cite|improve this answer











                                      $endgroup$



                                      If you want to think about units or dimensional analysis, then probably it is best to interpret 15% as



                                      $$ 15% = frac{text{$15$ units of X}}{text{$100$ units of X}} $$



                                      (I would read this as "15 units of X per 100 units of X".) For example, the Wikipedia page on dimensional analysis gives the example of debt-to-GDP ratio.
                                      $$ 90% text{ debt-to-GDP} = frac{text{$90$ dollars of debt}}{text{per $100$ dollars of GDP}} $$



                                      Here both the top and bottom are dollars. But they are two different dollar measurements. So even though the percentage is a dimensionless quantity (dollars/dollars), keeping the units in mind may be wise. Similarly



                                      $$ 10% text{ full} = frac{text{$10$ liters of water}}{text{per $100$ liters of container}} . $$



                                      and so on. (edit) So for example, if you want to do a calculation like "How many liters of water are in a 2-gallon container that is 10% full", you do



                                      $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$3.78$ liters of container}}{text{$1$ gallon of container}} ~ cdot ~ frac{text{$10$ liters of water}}{text{$100$ liters of container}} . $$



                                      Of course you could have also done



                                      $$ text{$2$ gallons of container} ~ cdot ~ frac{text{$10$ gallons of water}}{text{$100$ gallons of container}} ~ cdot ~ frac{text{$3.78$ liters of water}}{text{$1$ gallon of water}} ~ cdot . $$







                                      share|cite|improve this answer














                                      share|cite|improve this answer



                                      share|cite|improve this answer








                                      edited 13 hours ago

























                                      answered 13 hours ago









                                      usulusul

                                      1,6921422




                                      1,6921422























                                          0












                                          $begingroup$

                                          I believe you can think of it both ways.



                                          It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.






                                          share|cite|improve this answer









                                          $endgroup$


















                                            0












                                            $begingroup$

                                            I believe you can think of it both ways.



                                            It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.






                                            share|cite|improve this answer









                                            $endgroup$
















                                              0












                                              0








                                              0





                                              $begingroup$

                                              I believe you can think of it both ways.



                                              It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.






                                              share|cite|improve this answer









                                              $endgroup$



                                              I believe you can think of it both ways.



                                              It’s a symbol for “parts of a hundred” that happens to have a constant value behind it, and at the same time it’s a constant that happens to have a symbolic meaning behind it.







                                              share|cite|improve this answer












                                              share|cite|improve this answer



                                              share|cite|improve this answer










                                              answered 16 hours ago









                                              Victor S.Victor S.

                                              31019




                                              31019























                                                  0












                                                  $begingroup$

                                                  I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.



                                                  In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.






                                                  share|cite|improve this answer









                                                  $endgroup$


















                                                    0












                                                    $begingroup$

                                                    I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.



                                                    In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.






                                                    share|cite|improve this answer









                                                    $endgroup$
















                                                      0












                                                      0








                                                      0





                                                      $begingroup$

                                                      I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.



                                                      In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.






                                                      share|cite|improve this answer









                                                      $endgroup$



                                                      I don't think it has a universally agreed nature.(Symbol,constant,or Unit, or else?) Even though it might have had a single nature at the moment it was created, after a long time usage by people, with non-mathematicans as the majority, its nature might be different among different people's point of view.



                                                      In my opinion, I would regard '%' equivalent to the phrase 'out of 100'. That means 15% is read as '15 out of 100' . However, I am pretty sure someone else will have his own interpretation on '%' which leads no contradiction to mine.







                                                      share|cite|improve this answer












                                                      share|cite|improve this answer



                                                      share|cite|improve this answer










                                                      answered 16 hours ago









                                                      Anson NGAnson NG

                                                      20819




                                                      20819























                                                          0












                                                          $begingroup$

                                                          It is not a constant. It can be thought of as a unit if you like, but is probably best thought of as merely a syntax. A phrasing I find effective is to say that they are different spellings of a number.



                                                          The reason it is not a constant is because it cannot be used in all situations where a constant could be used. For example, $100x$ cannot be meaningfully written as $frac{x}{%}$. Were $%$ to be a constant, that would be a reasonable thing to write. It would be as reasonable as writing $frac{x}{pi}$.



                                                          You can get away with thinking of percents as units. Like with your approach of treating it as a constant, the math tends to work out. However, it doesn't really work well as a unit in general. While the axiomization of units is still an open problem, it is typically not true that $100 m = 1 frac{m}{%}$ or $1 m = 100 mcdot %$. This makes it an awkward sort of unit.



                                                          I do see "%" used as a unit from time to time, but it's typically shorthand for a particular percentage. I might see a graph of a chemical reaction efficiency written as "%/mol". Indeed, this is using "%" as a unit, but in such a graph it would really be a shorthand for "percent efficiency of the reaction." The same graph might instead be labeled with "%yield/mol" without really changing the meaning any. In this case, I think it is clear that "%" is not really acting as a unit in the way you might be used to. It's really just a letter, no different than "a" or "q."



                                                          Instead, perhaps the most reliable way of treating percents is as an alternate spelling for a number when writing it down. This is a nuanced difference: it suggests that 10% and 0.1 are not just equal, they are in fact merely two ways of writing down the same number. This would be no different than how a programmer might write 0x1F to denote the number 31 in a base-16 notation, how a Chinese person might elect to write 三十一 to denote the same number, or how we might write "thirty one." They are merely different ways of writing the same number.



                                                          This is a subtle difference, but sometimes it can be helpful. For example, at some point you will come across the proof that 0.9999.... = 1.0. This proof is very disconcerting at first, because you assume 0.9999... and 1.0 are two distinct numbers, so they could never be equal. But when you really dig into the meaning of that funny little "..." symbol, you discover there's a better way to think of it. "0.9999..." and "1.0" are simply two spellings of the same number. One relies on an infinite series to acquire its meaning, while the other does not, but they mean the same number.






                                                          share|cite|improve this answer









                                                          $endgroup$


















                                                            0












                                                            $begingroup$

                                                            It is not a constant. It can be thought of as a unit if you like, but is probably best thought of as merely a syntax. A phrasing I find effective is to say that they are different spellings of a number.



                                                            The reason it is not a constant is because it cannot be used in all situations where a constant could be used. For example, $100x$ cannot be meaningfully written as $frac{x}{%}$. Were $%$ to be a constant, that would be a reasonable thing to write. It would be as reasonable as writing $frac{x}{pi}$.



                                                            You can get away with thinking of percents as units. Like with your approach of treating it as a constant, the math tends to work out. However, it doesn't really work well as a unit in general. While the axiomization of units is still an open problem, it is typically not true that $100 m = 1 frac{m}{%}$ or $1 m = 100 mcdot %$. This makes it an awkward sort of unit.



                                                            I do see "%" used as a unit from time to time, but it's typically shorthand for a particular percentage. I might see a graph of a chemical reaction efficiency written as "%/mol". Indeed, this is using "%" as a unit, but in such a graph it would really be a shorthand for "percent efficiency of the reaction." The same graph might instead be labeled with "%yield/mol" without really changing the meaning any. In this case, I think it is clear that "%" is not really acting as a unit in the way you might be used to. It's really just a letter, no different than "a" or "q."



                                                            Instead, perhaps the most reliable way of treating percents is as an alternate spelling for a number when writing it down. This is a nuanced difference: it suggests that 10% and 0.1 are not just equal, they are in fact merely two ways of writing down the same number. This would be no different than how a programmer might write 0x1F to denote the number 31 in a base-16 notation, how a Chinese person might elect to write 三十一 to denote the same number, or how we might write "thirty one." They are merely different ways of writing the same number.



                                                            This is a subtle difference, but sometimes it can be helpful. For example, at some point you will come across the proof that 0.9999.... = 1.0. This proof is very disconcerting at first, because you assume 0.9999... and 1.0 are two distinct numbers, so they could never be equal. But when you really dig into the meaning of that funny little "..." symbol, you discover there's a better way to think of it. "0.9999..." and "1.0" are simply two spellings of the same number. One relies on an infinite series to acquire its meaning, while the other does not, but they mean the same number.






                                                            share|cite|improve this answer









                                                            $endgroup$
















                                                              0












                                                              0








                                                              0





                                                              $begingroup$

                                                              It is not a constant. It can be thought of as a unit if you like, but is probably best thought of as merely a syntax. A phrasing I find effective is to say that they are different spellings of a number.



                                                              The reason it is not a constant is because it cannot be used in all situations where a constant could be used. For example, $100x$ cannot be meaningfully written as $frac{x}{%}$. Were $%$ to be a constant, that would be a reasonable thing to write. It would be as reasonable as writing $frac{x}{pi}$.



                                                              You can get away with thinking of percents as units. Like with your approach of treating it as a constant, the math tends to work out. However, it doesn't really work well as a unit in general. While the axiomization of units is still an open problem, it is typically not true that $100 m = 1 frac{m}{%}$ or $1 m = 100 mcdot %$. This makes it an awkward sort of unit.



                                                              I do see "%" used as a unit from time to time, but it's typically shorthand for a particular percentage. I might see a graph of a chemical reaction efficiency written as "%/mol". Indeed, this is using "%" as a unit, but in such a graph it would really be a shorthand for "percent efficiency of the reaction." The same graph might instead be labeled with "%yield/mol" without really changing the meaning any. In this case, I think it is clear that "%" is not really acting as a unit in the way you might be used to. It's really just a letter, no different than "a" or "q."



                                                              Instead, perhaps the most reliable way of treating percents is as an alternate spelling for a number when writing it down. This is a nuanced difference: it suggests that 10% and 0.1 are not just equal, they are in fact merely two ways of writing down the same number. This would be no different than how a programmer might write 0x1F to denote the number 31 in a base-16 notation, how a Chinese person might elect to write 三十一 to denote the same number, or how we might write "thirty one." They are merely different ways of writing the same number.



                                                              This is a subtle difference, but sometimes it can be helpful. For example, at some point you will come across the proof that 0.9999.... = 1.0. This proof is very disconcerting at first, because you assume 0.9999... and 1.0 are two distinct numbers, so they could never be equal. But when you really dig into the meaning of that funny little "..." symbol, you discover there's a better way to think of it. "0.9999..." and "1.0" are simply two spellings of the same number. One relies on an infinite series to acquire its meaning, while the other does not, but they mean the same number.






                                                              share|cite|improve this answer









                                                              $endgroup$



                                                              It is not a constant. It can be thought of as a unit if you like, but is probably best thought of as merely a syntax. A phrasing I find effective is to say that they are different spellings of a number.



                                                              The reason it is not a constant is because it cannot be used in all situations where a constant could be used. For example, $100x$ cannot be meaningfully written as $frac{x}{%}$. Were $%$ to be a constant, that would be a reasonable thing to write. It would be as reasonable as writing $frac{x}{pi}$.



                                                              You can get away with thinking of percents as units. Like with your approach of treating it as a constant, the math tends to work out. However, it doesn't really work well as a unit in general. While the axiomization of units is still an open problem, it is typically not true that $100 m = 1 frac{m}{%}$ or $1 m = 100 mcdot %$. This makes it an awkward sort of unit.



                                                              I do see "%" used as a unit from time to time, but it's typically shorthand for a particular percentage. I might see a graph of a chemical reaction efficiency written as "%/mol". Indeed, this is using "%" as a unit, but in such a graph it would really be a shorthand for "percent efficiency of the reaction." The same graph might instead be labeled with "%yield/mol" without really changing the meaning any. In this case, I think it is clear that "%" is not really acting as a unit in the way you might be used to. It's really just a letter, no different than "a" or "q."



                                                              Instead, perhaps the most reliable way of treating percents is as an alternate spelling for a number when writing it down. This is a nuanced difference: it suggests that 10% and 0.1 are not just equal, they are in fact merely two ways of writing down the same number. This would be no different than how a programmer might write 0x1F to denote the number 31 in a base-16 notation, how a Chinese person might elect to write 三十一 to denote the same number, or how we might write "thirty one." They are merely different ways of writing the same number.



                                                              This is a subtle difference, but sometimes it can be helpful. For example, at some point you will come across the proof that 0.9999.... = 1.0. This proof is very disconcerting at first, because you assume 0.9999... and 1.0 are two distinct numbers, so they could never be equal. But when you really dig into the meaning of that funny little "..." symbol, you discover there's a better way to think of it. "0.9999..." and "1.0" are simply two spellings of the same number. One relies on an infinite series to acquire its meaning, while the other does not, but they mean the same number.







                                                              share|cite|improve this answer












                                                              share|cite|improve this answer



                                                              share|cite|improve this answer










                                                              answered 7 hours ago









                                                              Cort AmmonCort Ammon

                                                              2,401716




                                                              2,401716























                                                                  0












                                                                  $begingroup$

                                                                  It is just a notation i.e. a way of expressing numbers, e.g.



                                                                  $0.01 = 1% =10^{-2} = 1text{e-}02$



                                                                  nothing more. This is also why it is said to be dimensionless.



                                                                  There is absolutely nothing wrong in saying that someone is $20$ or $2000%$ years old, unusual admittedly.






                                                                  share|cite|improve this answer











                                                                  $endgroup$


















                                                                    0












                                                                    $begingroup$

                                                                    It is just a notation i.e. a way of expressing numbers, e.g.



                                                                    $0.01 = 1% =10^{-2} = 1text{e-}02$



                                                                    nothing more. This is also why it is said to be dimensionless.



                                                                    There is absolutely nothing wrong in saying that someone is $20$ or $2000%$ years old, unusual admittedly.






                                                                    share|cite|improve this answer











                                                                    $endgroup$
















                                                                      0












                                                                      0








                                                                      0





                                                                      $begingroup$

                                                                      It is just a notation i.e. a way of expressing numbers, e.g.



                                                                      $0.01 = 1% =10^{-2} = 1text{e-}02$



                                                                      nothing more. This is also why it is said to be dimensionless.



                                                                      There is absolutely nothing wrong in saying that someone is $20$ or $2000%$ years old, unusual admittedly.






                                                                      share|cite|improve this answer











                                                                      $endgroup$



                                                                      It is just a notation i.e. a way of expressing numbers, e.g.



                                                                      $0.01 = 1% =10^{-2} = 1text{e-}02$



                                                                      nothing more. This is also why it is said to be dimensionless.



                                                                      There is absolutely nothing wrong in saying that someone is $20$ or $2000%$ years old, unusual admittedly.







                                                                      share|cite|improve this answer














                                                                      share|cite|improve this answer



                                                                      share|cite|improve this answer








                                                                      edited 6 hours ago

























                                                                      answered 6 hours ago









                                                                      keepAlivekeepAlive

                                                                      178110




                                                                      178110























                                                                          0












                                                                          $begingroup$

                                                                          It's often convenient to write $x%$ for $x/100$. The notation $xy$ is also used for the product of $x$ and $y$ (whether numbers, functions, elements of a group, etc.), and these give the same result if you formally set $% = 1/100$. On the other hand, it would be bizarre to write "$1/%$ is divisible by $5$" or "$% + sqrt{%} = 0.11$", etc. There's nothing inherently wrong with abusing notation; I have no problem writing $0$ for the integer $0$, the real number $0$, the zero function, the zero element in a vector space, etc. But there's also nothing particularly noteworthy or profound in doing so.






                                                                          share|cite|improve this answer









                                                                          $endgroup$


















                                                                            0












                                                                            $begingroup$

                                                                            It's often convenient to write $x%$ for $x/100$. The notation $xy$ is also used for the product of $x$ and $y$ (whether numbers, functions, elements of a group, etc.), and these give the same result if you formally set $% = 1/100$. On the other hand, it would be bizarre to write "$1/%$ is divisible by $5$" or "$% + sqrt{%} = 0.11$", etc. There's nothing inherently wrong with abusing notation; I have no problem writing $0$ for the integer $0$, the real number $0$, the zero function, the zero element in a vector space, etc. But there's also nothing particularly noteworthy or profound in doing so.






                                                                            share|cite|improve this answer









                                                                            $endgroup$
















                                                                              0












                                                                              0








                                                                              0





                                                                              $begingroup$

                                                                              It's often convenient to write $x%$ for $x/100$. The notation $xy$ is also used for the product of $x$ and $y$ (whether numbers, functions, elements of a group, etc.), and these give the same result if you formally set $% = 1/100$. On the other hand, it would be bizarre to write "$1/%$ is divisible by $5$" or "$% + sqrt{%} = 0.11$", etc. There's nothing inherently wrong with abusing notation; I have no problem writing $0$ for the integer $0$, the real number $0$, the zero function, the zero element in a vector space, etc. But there's also nothing particularly noteworthy or profound in doing so.






                                                                              share|cite|improve this answer









                                                                              $endgroup$



                                                                              It's often convenient to write $x%$ for $x/100$. The notation $xy$ is also used for the product of $x$ and $y$ (whether numbers, functions, elements of a group, etc.), and these give the same result if you formally set $% = 1/100$. On the other hand, it would be bizarre to write "$1/%$ is divisible by $5$" or "$% + sqrt{%} = 0.11$", etc. There's nothing inherently wrong with abusing notation; I have no problem writing $0$ for the integer $0$, the real number $0$, the zero function, the zero element in a vector space, etc. But there's also nothing particularly noteworthy or profound in doing so.







                                                                              share|cite|improve this answer












                                                                              share|cite|improve this answer



                                                                              share|cite|improve this answer










                                                                              answered 4 hours ago









                                                                              anomalyanomaly

                                                                              17.6k42666




                                                                              17.6k42666






















                                                                                  Rudolph Gottesheim is a new contributor. Be nice, and check out our Code of Conduct.










                                                                                  draft saved

                                                                                  draft discarded


















                                                                                  Rudolph Gottesheim is a new contributor. Be nice, and check out our Code of Conduct.













                                                                                  Rudolph Gottesheim is a new contributor. Be nice, and check out our Code of Conduct.












                                                                                  Rudolph Gottesheim is a new contributor. Be nice, and check out our Code of Conduct.
















                                                                                  Thanks for contributing an answer to Mathematics Stack Exchange!


                                                                                  • Please be sure to answer the question. Provide details and share your research!

                                                                                  But avoid



                                                                                  • Asking for help, clarification, or responding to other answers.

                                                                                  • Making statements based on opinion; back them up with references or personal experience.


                                                                                  Use MathJax to format equations. MathJax reference.


                                                                                  To learn more, see our tips on writing great answers.




                                                                                  draft saved


                                                                                  draft discarded














                                                                                  StackExchange.ready(
                                                                                  function () {
                                                                                  StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmath.stackexchange.com%2fquestions%2f3122554%2fis-the-percentage-symbol-a-constant%23new-answer', 'question_page');
                                                                                  }
                                                                                  );

                                                                                  Post as a guest















                                                                                  Required, but never shown





















































                                                                                  Required, but never shown














                                                                                  Required, but never shown












                                                                                  Required, but never shown







                                                                                  Required, but never shown

































                                                                                  Required, but never shown














                                                                                  Required, but never shown












                                                                                  Required, but never shown







                                                                                  Required, but never shown







                                                                                  Popular posts from this blog

                                                                                  How to label and detect the document text images

                                                                                  Vallis Paradisi

                                                                                  Tabula Rosettana