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?






output-formatting 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?






    output-formatting 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?






      output-formatting 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?






      output-formatting number-form




      output-formatting number-form






      share|improve this question















      share|improve this question













      share|improve this question




      share|improve this question








      edited 1 min 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











            $endgroup$














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              2 Answers
              2






              active

              oldest

              votes








              2 Answers
              2






              active

              oldest

              votes









              active

              oldest

              votes






              active

              oldest

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              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 7 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 24 mins ago

























                          answered 1 hour ago









                          m_goldbergm_goldberg

                          88.4k872199




                          88.4k872199






























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