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












2












$begingroup$


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?






printing number-form







share|improve this question











$endgroup$

















    2












    $begingroup$


    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?






    printing number-form







    share|improve this question











    $endgroup$















      2












      2








      2





      $begingroup$


      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?






      printing number-form







      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?






      printing number-form




      printing number-form






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 34 mins ago









      m_goldberg

      88.4k872199




      88.4k872199










      asked 7 hours ago









      zyyzyy

      1236




      1236






















          2 Answers
          2






          active

          oldest

          votes


















          5












          $begingroup$

          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











          $endgroup$





















            1












            $begingroup$

            StringForm is very old. It goes all the back to V1.0, released in 1988, It represents an attempt by WRI to have a 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 Roe. It does 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 harder to do and requires more care.






            share|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: "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

























              2 Answers
              2






              active

              oldest

              votes








              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

              votes









              5












              $begingroup$

              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












                $begingroup$

                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












                  5








                  5





                  $begingroup$

                  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 6 hours ago

























                  answered 7 hours ago









                  RomanRoman

                  4,91011130




                  4,91011130























                      1












                      $begingroup$

                      StringForm is very old. It goes all the back to V1.0, released in 1988, It represents an attempt by WRI to have a 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 Roe. It does 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 harder to do and requires more care.






                      share|improve this answer











                      $endgroup$


















                        1












                        $begingroup$

                        StringForm is very old. It goes all the back to V1.0, released in 1988, It represents an attempt by WRI to have a 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 Roe. It does 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 harder to do and requires more care.






                        share|improve this answer











                        $endgroup$
















                          1












                          1








                          1





                          $begingroup$

                          StringForm is very old. It goes all the back to V1.0, released in 1988, It represents an attempt by WRI to have a 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 Roe. It does 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 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 a 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 Roe. It does 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 harder to do and requires more care.







                          share|improve this answer














                          share|improve this answer



                          share|improve this answer








                          edited 20 mins ago

























                          answered 1 hour ago









                          m_goldbergm_goldberg

                          88.4k872199




                          88.4k872199






























                              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

                              Ponta tanko

                              Image
                              Usona ponta tanko M60A1 Ponta tanko estas, simile kiel kirasita savveturilo, inter specialaj kirasitaj transportiloj. Kiel pontaj tankoj eblas konsideri ĉiujn memmovigaj rimedoj ebligantaj superi obstaklojn ĝis larĝeco 24 metroj rekte en spaco de bataloperacoj. Ties ĉefa tasko estas ebligi al la propraj taĉmentoj daŭrigi en rapida antaŭenirado sen senbezona reteniĝo. El tio pli-malpli rezultas taktikaj-teknikaj postuloj, kiujn ili devas plenumi. Precipe temas pri kapablo operacii komune kun unue-sinsekvaj taĉmentoj kaj transpontigi obstaklojn dum kelke da minutoj. This page is only for reference, If you need detailed information, please check here
                              Read more

                              Tantalo (mitologio)

                              Image
                              Ĉi tiu artikolo temas pri mitologio. Por aliaj signifoj vidu la paĝon Tantalo (apartigilo) . Tantalo , laŭ Gioacchino Assereto. Laŭ la helena mitologio, Tantalo (el la greka Τάνταλος , ŝancelanta aŭ tre malfeliĉa ) estis filo de Zeŭso kaj la oceanidino Pluto, laŭ la plej divastigata versio. Li estis reĝo de Frigio [1] aŭ de la monto Sipilo, en Lidio (Malgrandazio) [2] kaj post sia morto li suferis eternan torturadon ĉe la Tartaro, la plej profunda parto de Hadeso, rezervita por la plej perversaj homoj. Tamen, kelkaj rakontoj asertas ke li estis reĝo de Argo aŭ de Korinto [3] , aŭ ke li migris norden el la monto Sipilo por akiri la tronon de Paflagonio, el kie Ilo forpelis lin pro tio, ke Tantalo forkaptis kaj seksperfortis lian fraton Ganimedon [4] , kaj tiel ofendis la diojn. Verŝajne li ankaŭ regis urbon en okcidenta Anatolio, kiun oni nomis Tantalis [5] pro li, aŭ Sipilo , pro la monto sur kies flanko ankoraŭ staras ĝiaj ruinaĵoj [6] . Laŭ la geografiisto Strabo,...
                              Read more

                              Erzsébet Schaár

                              Image
                              Erzsébet Schaár Memportreto de Erzsébet Schaár en Pécs Personaj informoj Naskiĝo 27-an de julio 1908 ( 1908-07-27 ) en Budafok Morto 29-an de aŭgusto 1975 ( 1975-08-29 ) (67-jara) en Budapeŝto Ŝtataneco Hungario Profesio skulptisto Familianoj Edz(in)o Tibor Vilt v   •   d   •   r Erzsébet Schaár [erĵEbet ŝAr], laŭ hungarlingve kutima sinsekvo Schaár Erzsébet estis hungara skulptisto. Ŝia edzo estis Tibor Vilt. Déryné Széppataki Róza en Miskolc fare de Erzsébet Schaár Erzsébet Schaár [1] naskiĝis la 27-an de julio 1908 en Budafok, ŝi mortis la 29-an de aŭgusto 1975 en Budapeŝto. Enhavo 1 Biografio 2 Elektitaj solaj ekspozicioj 3 Elektitaj kolektivaj ekspozicioj 4 Elektitaj skulptaĵoj 5 Elektitaj disĉiploj 6 Fontoj 7 Referencoj Biografio | Erzsébet Schaár studis en Industriarta Lernejo, poste en Reĝa Belarta Altlernejo (1924-1926). Ŝia ĉefinstruisto estis Zsig...
                              Read more