Why km$^2$ and not (km)$^2$?











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Why don't km$^2$, cm$^3ldots$ follow the precedence rule of power over product ? One should write (km)$^2$ since it is one million square meters.






physics unit-of-measure







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  • km doesn't represent multiplication... well, you know... I guess it could... huh. Anyway, km is an abbreviation for a word where kilo is a suffix. It's not typically thought of as multiplication.
    – Robert Wolfe
    Nov 27 at 17:41








  • 1




    Because you're not actually doing arithmetic with the units in the same way toy do arithmetic with their quantities.
    – Michael McGovern
    Nov 27 at 17:42










  • Anyway, what $mathrm{km}^2$ means is actually $(mathrm{km})^2$ instead of $mathrm{k(m)}^2$
    – rafa11111
    Nov 27 at 17:47















up vote
1
down vote

favorite












Why don't km$^2$, cm$^3ldots$ follow the precedence rule of power over product ? One should write (km)$^2$ since it is one million square meters.






physics unit-of-measure







share|cite|improve this question
























  • km doesn't represent multiplication... well, you know... I guess it could... huh. Anyway, km is an abbreviation for a word where kilo is a suffix. It's not typically thought of as multiplication.
    – Robert Wolfe
    Nov 27 at 17:41








  • 1




    Because you're not actually doing arithmetic with the units in the same way toy do arithmetic with their quantities.
    – Michael McGovern
    Nov 27 at 17:42










  • Anyway, what $mathrm{km}^2$ means is actually $(mathrm{km})^2$ instead of $mathrm{k(m)}^2$
    – rafa11111
    Nov 27 at 17:47













up vote
1
down vote

favorite









up vote
1
down vote

favorite











Why don't km$^2$, cm$^3ldots$ follow the precedence rule of power over product ? One should write (km)$^2$ since it is one million square meters.






physics unit-of-measure







share|cite|improve this question















Why don't km$^2$, cm$^3ldots$ follow the precedence rule of power over product ? One should write (km)$^2$ since it is one million square meters.






physics unit-of-measure




physics unit-of-measure






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edited Nov 27 at 17:45









Larry

1,2902722




1,2902722










asked Nov 27 at 17:39









Poor Standard

114




114












  • km doesn't represent multiplication... well, you know... I guess it could... huh. Anyway, km is an abbreviation for a word where kilo is a suffix. It's not typically thought of as multiplication.
    – Robert Wolfe
    Nov 27 at 17:41








  • 1




    Because you're not actually doing arithmetic with the units in the same way toy do arithmetic with their quantities.
    – Michael McGovern
    Nov 27 at 17:42










  • Anyway, what $mathrm{km}^2$ means is actually $(mathrm{km})^2$ instead of $mathrm{k(m)}^2$
    – rafa11111
    Nov 27 at 17:47


















  • km doesn't represent multiplication... well, you know... I guess it could... huh. Anyway, km is an abbreviation for a word where kilo is a suffix. It's not typically thought of as multiplication.
    – Robert Wolfe
    Nov 27 at 17:41








  • 1




    Because you're not actually doing arithmetic with the units in the same way toy do arithmetic with their quantities.
    – Michael McGovern
    Nov 27 at 17:42










  • Anyway, what $mathrm{km}^2$ means is actually $(mathrm{km})^2$ instead of $mathrm{k(m)}^2$
    – rafa11111
    Nov 27 at 17:47
















km doesn't represent multiplication... well, you know... I guess it could... huh. Anyway, km is an abbreviation for a word where kilo is a suffix. It's not typically thought of as multiplication.
– Robert Wolfe
Nov 27 at 17:41






km doesn't represent multiplication... well, you know... I guess it could... huh. Anyway, km is an abbreviation for a word where kilo is a suffix. It's not typically thought of as multiplication.
– Robert Wolfe
Nov 27 at 17:41






1




1




Because you're not actually doing arithmetic with the units in the same way toy do arithmetic with their quantities.
– Michael McGovern
Nov 27 at 17:42




Because you're not actually doing arithmetic with the units in the same way toy do arithmetic with their quantities.
– Michael McGovern
Nov 27 at 17:42












Anyway, what $mathrm{km}^2$ means is actually $(mathrm{km})^2$ instead of $mathrm{k(m)}^2$
– rafa11111
Nov 27 at 17:47




Anyway, what $mathrm{km}^2$ means is actually $(mathrm{km})^2$ instead of $mathrm{k(m)}^2$
– rafa11111
Nov 27 at 17:47










4 Answers
4






active

oldest

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up vote
0
down vote



accepted










@zahbaz 's answer is correct. It's a convention, and a good one. I think the commenters who say the reason is that "km" is just a single word and not "$1000 times$ m" are missing an important point. You can indeed and often should think of the metric prefixes for size as factors - and remember that the convention for operator precedence (exponentiation over multiplication) doesn't apply in this context.






share|cite|improve this answer




























    up vote
    3
    down vote













    The convention is that units are treated as a single object with their metric prefixes attached. This cuts back on excessive notation, like parentheses. That is, with km we are not treating k and m as separate symbols representing $1000$ and meters respectively.






    share|cite|improve this answer






























      up vote
      3
      down vote













      It has been standardized like this in the International System of Units (SI), see https://www.bipm.org/en/publications/si-brochure/chapter3.html




      The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.







      share|cite|improve this answer





















      • thanks for the refs
        – Poor Standard
        Nov 27 at 20:05


















      up vote
      1
      down vote













      $text{km}$ stands for kilometer, not for "$text ktimestext m$" where "$text k$" would denote the constant $1000$.






      share|cite|improve this answer





















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        4 Answers
        4






        active

        oldest

        votes








        4 Answers
        4






        active

        oldest

        votes









        active

        oldest

        votes






        active

        oldest

        votes








        up vote
        0
        down vote



        accepted










        @zahbaz 's answer is correct. It's a convention, and a good one. I think the commenters who say the reason is that "km" is just a single word and not "$1000 times$ m" are missing an important point. You can indeed and often should think of the metric prefixes for size as factors - and remember that the convention for operator precedence (exponentiation over multiplication) doesn't apply in this context.






        share|cite|improve this answer

























          up vote
          0
          down vote



          accepted










          @zahbaz 's answer is correct. It's a convention, and a good one. I think the commenters who say the reason is that "km" is just a single word and not "$1000 times$ m" are missing an important point. You can indeed and often should think of the metric prefixes for size as factors - and remember that the convention for operator precedence (exponentiation over multiplication) doesn't apply in this context.






          share|cite|improve this answer























            up vote
            0
            down vote



            accepted







            up vote
            0
            down vote



            accepted






            @zahbaz 's answer is correct. It's a convention, and a good one. I think the commenters who say the reason is that "km" is just a single word and not "$1000 times$ m" are missing an important point. You can indeed and often should think of the metric prefixes for size as factors - and remember that the convention for operator precedence (exponentiation over multiplication) doesn't apply in this context.






            share|cite|improve this answer












            @zahbaz 's answer is correct. It's a convention, and a good one. I think the commenters who say the reason is that "km" is just a single word and not "$1000 times$ m" are missing an important point. You can indeed and often should think of the metric prefixes for size as factors - and remember that the convention for operator precedence (exponentiation over multiplication) doesn't apply in this context.







            share|cite|improve this answer












            share|cite|improve this answer



            share|cite|improve this answer










            answered Nov 27 at 17:57









            Ethan Bolker

            40.5k545107




            40.5k545107






















                up vote
                3
                down vote













                The convention is that units are treated as a single object with their metric prefixes attached. This cuts back on excessive notation, like parentheses. That is, with km we are not treating k and m as separate symbols representing $1000$ and meters respectively.






                share|cite|improve this answer



























                  up vote
                  3
                  down vote













                  The convention is that units are treated as a single object with their metric prefixes attached. This cuts back on excessive notation, like parentheses. That is, with km we are not treating k and m as separate symbols representing $1000$ and meters respectively.






                  share|cite|improve this answer

























                    up vote
                    3
                    down vote










                    up vote
                    3
                    down vote









                    The convention is that units are treated as a single object with their metric prefixes attached. This cuts back on excessive notation, like parentheses. That is, with km we are not treating k and m as separate symbols representing $1000$ and meters respectively.






                    share|cite|improve this answer














                    The convention is that units are treated as a single object with their metric prefixes attached. This cuts back on excessive notation, like parentheses. That is, with km we are not treating k and m as separate symbols representing $1000$ and meters respectively.







                    share|cite|improve this answer














                    share|cite|improve this answer



                    share|cite|improve this answer








                    edited Nov 27 at 17:56

























                    answered Nov 27 at 17:48









                    zahbaz

                    8,18921937




                    8,18921937






















                        up vote
                        3
                        down vote













                        It has been standardized like this in the International System of Units (SI), see https://www.bipm.org/en/publications/si-brochure/chapter3.html




                        The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.







                        share|cite|improve this answer





















                        • thanks for the refs
                          – Poor Standard
                          Nov 27 at 20:05















                        up vote
                        3
                        down vote













                        It has been standardized like this in the International System of Units (SI), see https://www.bipm.org/en/publications/si-brochure/chapter3.html




                        The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.







                        share|cite|improve this answer





















                        • thanks for the refs
                          – Poor Standard
                          Nov 27 at 20:05













                        up vote
                        3
                        down vote










                        up vote
                        3
                        down vote









                        It has been standardized like this in the International System of Units (SI), see https://www.bipm.org/en/publications/si-brochure/chapter3.html




                        The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.







                        share|cite|improve this answer












                        It has been standardized like this in the International System of Units (SI), see https://www.bipm.org/en/publications/si-brochure/chapter3.html




                        The grouping formed by a prefix symbol attached to a unit symbol constitutes a new inseparable unit symbol (forming a multiple or submultiple of the unit concerned) that can be raised to a positive or negative power and that can be combined with other unit symbols to form compound unit symbols.








                        share|cite|improve this answer












                        share|cite|improve this answer



                        share|cite|improve this answer










                        answered Nov 27 at 17:59









                        Reinhard Meier

                        2,807210




                        2,807210












                        • thanks for the refs
                          – Poor Standard
                          Nov 27 at 20:05


















                        • thanks for the refs
                          – Poor Standard
                          Nov 27 at 20:05
















                        thanks for the refs
                        – Poor Standard
                        Nov 27 at 20:05




                        thanks for the refs
                        – Poor Standard
                        Nov 27 at 20:05










                        up vote
                        1
                        down vote













                        $text{km}$ stands for kilometer, not for "$text ktimestext m$" where "$text k$" would denote the constant $1000$.






                        share|cite|improve this answer

























                          up vote
                          1
                          down vote













                          $text{km}$ stands for kilometer, not for "$text ktimestext m$" where "$text k$" would denote the constant $1000$.






                          share|cite|improve this answer























                            up vote
                            1
                            down vote










                            up vote
                            1
                            down vote









                            $text{km}$ stands for kilometer, not for "$text ktimestext m$" where "$text k$" would denote the constant $1000$.






                            share|cite|improve this answer












                            $text{km}$ stands for kilometer, not for "$text ktimestext m$" where "$text k$" would denote the constant $1000$.







                            share|cite|improve this answer












                            share|cite|improve this answer



                            share|cite|improve this answer










                            answered Nov 27 at 17:49









                            Yves Daoust

                            123k668219




                            123k668219






























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