Why do I get badly formatted numerical results when I use StringForm?












3












$begingroup$


The following example prints the square and cube of numbers from 0.5 to 6



Do[
Print[StringForm["the square of `` is ``, the cube of it is ``", i, i^2, i^3]],
{i, 0.5, 6, 0.1}]


It should be fine, however, for 0.7 Mathematica prints




the square of 0.7` is 0.48999999999999994`, the cube of it is 0.3429999999999999`



Why is the square of 0.7 approximated by 0.48999999999999994? No approximation will be made if I did not use StringForm, why is that?



By the way, there is a ` at the end of each output number, why is it there?










share|improve this question











$endgroup$

















    3












    $begingroup$


    The following example prints the square and cube of numbers from 0.5 to 6



    Do[
    Print[StringForm["the square of `` is ``, the cube of it is ``", i, i^2, i^3]],
    {i, 0.5, 6, 0.1}]


    It should be fine, however, for 0.7 Mathematica prints




    the square of 0.7` is 0.48999999999999994`, the cube of it is 0.3429999999999999`



    Why is the square of 0.7 approximated by 0.48999999999999994? No approximation will be made if I did not use StringForm, why is that?



    By the way, there is a ` at the end of each output number, why is it there?










    share|improve this question











    $endgroup$















      3












      3








      3





      $begingroup$


      The following example prints the square and cube of numbers from 0.5 to 6



      Do[
      Print[StringForm["the square of `` is ``, the cube of it is ``", i, i^2, i^3]],
      {i, 0.5, 6, 0.1}]


      It should be fine, however, for 0.7 Mathematica prints




      the square of 0.7` is 0.48999999999999994`, the cube of it is 0.3429999999999999`



      Why is the square of 0.7 approximated by 0.48999999999999994? No approximation will be made if I did not use StringForm, why is that?



      By the way, there is a ` at the end of each output number, why is it there?










      share|improve this question











      $endgroup$




      The following example prints the square and cube of numbers from 0.5 to 6



      Do[
      Print[StringForm["the square of `` is ``, the cube of it is ``", i, i^2, i^3]],
      {i, 0.5, 6, 0.1}]


      It should be fine, however, for 0.7 Mathematica prints




      the square of 0.7` is 0.48999999999999994`, the cube of it is 0.3429999999999999`



      Why is the square of 0.7 approximated by 0.48999999999999994? No approximation will be made if I did not use StringForm, why is that?



      By the way, there is a ` at the end of each output number, why is it there?







      output-formatting number-form






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited Apr 10 at 5:22









      m_goldberg

      88.7k873200




      88.7k873200










      asked Apr 9 at 21:58









      zyyzyy

      1286




      1286






















          4 Answers
          4






          active

          oldest

          votes


















          8












          $begingroup$

          This is what happens when you use IEEE-754 double-precision math instead of exact math.



          StringForm, InputForm, FullForm etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.



          Other number display functions, like NumberForm, show fewer digits. The internal representation of the number doesn't change though.



          The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.



          You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:



          Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
          N[i], N[i^2], N[i^3]]], {i, 1/2, 6, 1/10}]



          the square of 0.7` is 0.49`, the cube of it is 0.343`







          share|improve this answer











          $endgroup$





















            5












            $begingroup$

            StringForm is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.



            V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row. It does not have the problem with formatting machine numbers that you ran into by using StringForm.



            Here is how you can get your output with Row.



            Column[
            Table[
            Row[{"the square of ", i, " is ", i^2, ", the cube of it is ", i^3}],
            {i, 0.5, 1., .1}]]


            output



            One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:



            numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
            Style[
            Column[
            Table[
            Row[
            {"the square of ", numStyle[i], " is ", numStyle[i^2],
            ", the cube of it is ", numStyle[i^3]}],
            {i, 0.5, 1., .1}]],
            FontFamily -> "Arial"]


            styled



            It isn't that you can't apply styles to StringForm output, but that it is harder to do and requires more care.






            share|improve this answer











            $endgroup$





















              2












              $begingroup$

              I would recommend looking at StringTemplate.



              Do[Print[StringTemplate[
              "the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], {i,
              0.5, 1, 0.1}]


              the square of 0.5 is 0.25, the cube of it is 0.125

              the square of 0.6 is 0.36, the cube of it is 0.216

              the square of 0.7 is 0.49, the cube of it is 0.343

              the square of 0.8 is 0.64, the cube of it is 0.512

              the square of 0.9 is 0.81, the cube of it is 0.729

              the square of 1. is 1., the cube of it is 1.





              share|improve this answer









              $endgroup$





















                1












                $begingroup$

                You can also use StandardForm, which is the standard format of output cells:



                Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
                {i, 0.5, 6, 0.1}]





                share|improve this answer









                $endgroup$














                  Your Answer








                  StackExchange.ready(function() {
                  var channelOptions = {
                  tags: "".split(" "),
                  id: "387"
                  };
                  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: false,
                  noModals: true,
                  showLowRepImageUploadWarning: true,
                  reputationToPostImages: null,
                  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
                  },
                  onDemand: true,
                  discardSelector: ".discard-answer"
                  ,immediatelyShowMarkdownHelp:true
                  });


                  }
                  });














                  draft saved

                  draft discarded


















                  StackExchange.ready(
                  function () {
                  StackExchange.openid.initPostLogin('.new-post-login', 'https%3a%2f%2fmathematica.stackexchange.com%2fquestions%2f194909%2fwhy-do-i-get-badly-formatted-numerical-results-when-i-use-stringform%23new-answer', 'question_page');
                  }
                  );

                  Post as a guest















                  Required, but never shown

























                  4 Answers
                  4






                  active

                  oldest

                  votes








                  4 Answers
                  4






                  active

                  oldest

                  votes









                  active

                  oldest

                  votes






                  active

                  oldest

                  votes









                  8












                  $begingroup$

                  This is what happens when you use IEEE-754 double-precision math instead of exact math.



                  StringForm, InputForm, FullForm etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.



                  Other number display functions, like NumberForm, show fewer digits. The internal representation of the number doesn't change though.



                  The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.



                  You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:



                  Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                  N[i], N[i^2], N[i^3]]], {i, 1/2, 6, 1/10}]



                  the square of 0.7` is 0.49`, the cube of it is 0.343`







                  share|improve this answer











                  $endgroup$


















                    8












                    $begingroup$

                    This is what happens when you use IEEE-754 double-precision math instead of exact math.



                    StringForm, InputForm, FullForm etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.



                    Other number display functions, like NumberForm, show fewer digits. The internal representation of the number doesn't change though.



                    The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.



                    You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:



                    Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                    N[i], N[i^2], N[i^3]]], {i, 1/2, 6, 1/10}]



                    the square of 0.7` is 0.49`, the cube of it is 0.343`







                    share|improve this answer











                    $endgroup$
















                      8












                      8








                      8





                      $begingroup$

                      This is what happens when you use IEEE-754 double-precision math instead of exact math.



                      StringForm, InputForm, FullForm etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.



                      Other number display functions, like NumberForm, show fewer digits. The internal representation of the number doesn't change though.



                      The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.



                      You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:



                      Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                      N[i], N[i^2], N[i^3]]], {i, 1/2, 6, 1/10}]



                      the square of 0.7` is 0.49`, the cube of it is 0.343`







                      share|improve this answer











                      $endgroup$



                      This is what happens when you use IEEE-754 double-precision math instead of exact math.



                      StringForm, InputForm, FullForm etc. give you all possible digits of these IEEE-754 double-precision numbers used internally. This is no different from any other programming language.



                      Other number display functions, like NumberForm, show fewer digits. The internal representation of the number doesn't change though.



                      The backtick ` indicates a machine-precision number, which is usually (always?) an IEEE-754 double-precision number.



                      You can get the result you're looking for by doing the conversion to numerical values after the squaring/cubing:



                      Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                      N[i], N[i^2], N[i^3]]], {i, 1/2, 6, 1/10}]



                      the square of 0.7` is 0.49`, the cube of it is 0.343`








                      share|improve this answer














                      share|improve this answer



                      share|improve this answer








                      edited Apr 9 at 22:19

























                      answered Apr 9 at 22:08









                      RomanRoman

                      5,40311131




                      5,40311131























                          5












                          $begingroup$

                          StringForm is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.



                          V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row. It does not have the problem with formatting machine numbers that you ran into by using StringForm.



                          Here is how you can get your output with Row.



                          Column[
                          Table[
                          Row[{"the square of ", i, " is ", i^2, ", the cube of it is ", i^3}],
                          {i, 0.5, 1., .1}]]


                          output



                          One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:



                          numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
                          Style[
                          Column[
                          Table[
                          Row[
                          {"the square of ", numStyle[i], " is ", numStyle[i^2],
                          ", the cube of it is ", numStyle[i^3]}],
                          {i, 0.5, 1., .1}]],
                          FontFamily -> "Arial"]


                          styled



                          It isn't that you can't apply styles to StringForm output, but that it is harder to do and requires more care.






                          share|improve this answer











                          $endgroup$


















                            5












                            $begingroup$

                            StringForm is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.



                            V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row. It does not have the problem with formatting machine numbers that you ran into by using StringForm.



                            Here is how you can get your output with Row.



                            Column[
                            Table[
                            Row[{"the square of ", i, " is ", i^2, ", the cube of it is ", i^3}],
                            {i, 0.5, 1., .1}]]


                            output



                            One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:



                            numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
                            Style[
                            Column[
                            Table[
                            Row[
                            {"the square of ", numStyle[i], " is ", numStyle[i^2],
                            ", the cube of it is ", numStyle[i^3]}],
                            {i, 0.5, 1., .1}]],
                            FontFamily -> "Arial"]


                            styled



                            It isn't that you can't apply styles to StringForm output, but that it is harder to do and requires more care.






                            share|improve this answer











                            $endgroup$
















                              5












                              5








                              5





                              $begingroup$

                              StringForm is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.



                              V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row. It does not have the problem with formatting machine numbers that you ran into by using StringForm.



                              Here is how you can get your output with Row.



                              Column[
                              Table[
                              Row[{"the square of ", i, " is ", i^2, ", the cube of it is ", i^3}],
                              {i, 0.5, 1., .1}]]


                              output



                              One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:



                              numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
                              Style[
                              Column[
                              Table[
                              Row[
                              {"the square of ", numStyle[i], " is ", numStyle[i^2],
                              ", the cube of it is ", numStyle[i^3]}],
                              {i, 0.5, 1., .1}]],
                              FontFamily -> "Arial"]


                              styled



                              It isn't that you can't apply styles to StringForm output, but that it is harder to do and requires more care.






                              share|improve this answer











                              $endgroup$



                              StringForm is very old. It goes all the back to V1.0, released in 1988. It represents an attempt by WRI to have an IO formatter that would appeal to programmers familiar with C and similar programming languages.



                              V6.0, released in 2003, added formatting tools that are not only easier to use but which are better integrated into Mathematica's way of doing things. One of the new IO formatters was Row. It does not have the problem with formatting machine numbers that you ran into by using StringForm.



                              Here is how you can get your output with Row.



                              Column[
                              Table[
                              Row[{"the square of ", i, " is ", i^2, ", the cube of it is ", i^3}],
                              {i, 0.5, 1., .1}]]


                              output



                              One of the nice features of the newer IO formatting tools is that they allow styles to be applied at almost any level. For example:



                              numStyle[num_?NumericQ] := Style[num, Red, Bold, Italic]
                              Style[
                              Column[
                              Table[
                              Row[
                              {"the square of ", numStyle[i], " is ", numStyle[i^2],
                              ", the cube of it is ", numStyle[i^3]}],
                              {i, 0.5, 1., .1}]],
                              FontFamily -> "Arial"]


                              styled



                              It isn't that you can't apply styles to StringForm output, but that it is harder to do and requires more care.







                              share|improve this answer














                              share|improve this answer



                              share|improve this answer








                              edited Apr 10 at 5:23

























                              answered Apr 10 at 4:07









                              m_goldbergm_goldberg

                              88.7k873200




                              88.7k873200























                                  2












                                  $begingroup$

                                  I would recommend looking at StringTemplate.



                                  Do[Print[StringTemplate[
                                  "the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], {i,
                                  0.5, 1, 0.1}]


                                  the square of 0.5 is 0.25, the cube of it is 0.125

                                  the square of 0.6 is 0.36, the cube of it is 0.216

                                  the square of 0.7 is 0.49, the cube of it is 0.343

                                  the square of 0.8 is 0.64, the cube of it is 0.512

                                  the square of 0.9 is 0.81, the cube of it is 0.729

                                  the square of 1. is 1., the cube of it is 1.





                                  share|improve this answer









                                  $endgroup$


















                                    2












                                    $begingroup$

                                    I would recommend looking at StringTemplate.



                                    Do[Print[StringTemplate[
                                    "the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], {i,
                                    0.5, 1, 0.1}]


                                    the square of 0.5 is 0.25, the cube of it is 0.125

                                    the square of 0.6 is 0.36, the cube of it is 0.216

                                    the square of 0.7 is 0.49, the cube of it is 0.343

                                    the square of 0.8 is 0.64, the cube of it is 0.512

                                    the square of 0.9 is 0.81, the cube of it is 0.729

                                    the square of 1. is 1., the cube of it is 1.





                                    share|improve this answer









                                    $endgroup$
















                                      2












                                      2








                                      2





                                      $begingroup$

                                      I would recommend looking at StringTemplate.



                                      Do[Print[StringTemplate[
                                      "the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], {i,
                                      0.5, 1, 0.1}]


                                      the square of 0.5 is 0.25, the cube of it is 0.125

                                      the square of 0.6 is 0.36, the cube of it is 0.216

                                      the square of 0.7 is 0.49, the cube of it is 0.343

                                      the square of 0.8 is 0.64, the cube of it is 0.512

                                      the square of 0.9 is 0.81, the cube of it is 0.729

                                      the square of 1. is 1., the cube of it is 1.





                                      share|improve this answer









                                      $endgroup$



                                      I would recommend looking at StringTemplate.



                                      Do[Print[StringTemplate[
                                      "the square of `` is ``, the cube of it is ``"][i, i^2, i^3]], {i,
                                      0.5, 1, 0.1}]


                                      the square of 0.5 is 0.25, the cube of it is 0.125

                                      the square of 0.6 is 0.36, the cube of it is 0.216

                                      the square of 0.7 is 0.49, the cube of it is 0.343

                                      the square of 0.8 is 0.64, the cube of it is 0.512

                                      the square of 0.9 is 0.81, the cube of it is 0.729

                                      the square of 1. is 1., the cube of it is 1.






                                      share|improve this answer












                                      share|improve this answer



                                      share|improve this answer










                                      answered Apr 10 at 14:35









                                      chuychuy

                                      9,4731841




                                      9,4731841























                                          1












                                          $begingroup$

                                          You can also use StandardForm, which is the standard format of output cells:



                                          Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                                          StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
                                          {i, 0.5, 6, 0.1}]





                                          share|improve this answer









                                          $endgroup$


















                                            1












                                            $begingroup$

                                            You can also use StandardForm, which is the standard format of output cells:



                                            Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                                            StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
                                            {i, 0.5, 6, 0.1}]





                                            share|improve this answer









                                            $endgroup$
















                                              1












                                              1








                                              1





                                              $begingroup$

                                              You can also use StandardForm, which is the standard format of output cells:



                                              Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                                              StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
                                              {i, 0.5, 6, 0.1}]





                                              share|improve this answer









                                              $endgroup$



                                              You can also use StandardForm, which is the standard format of output cells:



                                              Do[Print[StringForm["the square of `` is ``, the cube of it is ``", 
                                              StandardForm[i], StandardForm[i^2], StandardForm[i^3]]],
                                              {i, 0.5, 6, 0.1}]






                                              share|improve this answer












                                              share|improve this answer



                                              share|improve this answer










                                              answered Apr 11 at 2:14









                                              Michael E2Michael E2

                                              151k12203482




                                              151k12203482






























                                                  draft saved

                                                  draft discarded




















































                                                  Thanks for contributing an answer to Mathematica 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%2fmathematica.stackexchange.com%2fquestions%2f194909%2fwhy-do-i-get-badly-formatted-numerical-results-when-i-use-stringform%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

                                                  Plaza Victoria

                                                  Puebla de Zaragoza

                                                  Musa