February 1993/Real-Number Approximation for Real Programmers/Table 1

Table 1 Comparing the accuracy of radix-10 versus "hand-picked" rational approximations of p. (Overlined digits signify a repeating sequence.)

    Radix-10         "Hand Picked"  Value         Percent
      Ratio              Ratio                     Error

      3 / 1                         3              -4.5

     31 / 10                        3.1            -1.3

    314 / 100                       3.14           -0.051
                                   
                        22 / 7      3.142857       +0.040

   3142 / 1000                      3.142          +0.013

                       333 / 106    3.1415094...   -0.0026

  31416 / 10000                     3.1416         +0.00023

 314159 / 100000                    3.14159        0.000084

3141593 / 1000000                   3.141593       +0.000011

                       355 / 113    3.1415929...   +0.0000085

31415927 / 10000000                 3.1415927      +0.0000015