What does Pi equal to What is the approximation of pi in a fraction form. I am very curious to know what it is. I have been seeing pi almost everywhere.

Question

Nicolas Calhoun · Accepted Answer

The idea here is that you can compute the continued fraction of   π and then truncate it somewhere to achieve an approximation of   π  =  3.141592653589  …  π  =  3  +                                                  1                                                                  7          +                                                                                                                  1                                                                                                                                                  15                  +                                                                                                                                                                                  1                                                                                                                                                                                                                                  1                          +                                                                                                                                                                                                                                                  1                                                                                                                                                                                                                                                                                                                  292                                  +                                                                                                                                                                                                                                                                                                                  1                                                                                                                                                                                                                                                                                                                                                                                                  1                                          +                                                                                                                                                                                                                                                                                                                                                                                  1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1                                                  +                                                                                                                                                                                                                                                                                                                                                                                                                                                  1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1                                                          +                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  1                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  2                                                                  +                                                                  ⋯                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                The further along you truncate it, the more accurate your approximation. If we cut it off pretty early (at 7), we get the classic        22    7   approximation:  π  ≈  3  +      1    7    =      22    7    =  3.14      28571428571    …  If we cut it off later (say at 292), we get a better approximation:                    π                            ≈        3        +                                                                                                  1                                                                                                                              7                +                                                                                                                                                                  1                                                                                                                                                                                                              15                        +                                                                                                                                                                                                                                  1                                                                                                                                                                                                                                                                                              1                                +                                                                  1                                  292                                                                                                                                                                                                                                                                                                              ≈        3        +                                                                                                  1                                                                                                                              7                +                                                                                                                                                                  1                                                                                                                                                                                                              15                        +                                                  292                          293                                                                                                                                                                                          ≈        3        +                                                                                                  1                                                                                                                              7                +                                  293                  4687                                                                                                      ≈        3        +                                                                                                  4687                                                                                                                              33102                                                                        π                            ≈                  103993          33102                =        3.141592653                  0119          …                    You can use this method to get a rational number that is as close to π as you need.

Augustus Acevedo · Accepted Answer

I would say       314159265    100000000