What is the fraction representation of 3.14159265359

I think "the" is not the correct word here. There is no largely accurate fraction representation of pi without having to use an infinitely large number of digits in both the numerator and denominator. An approximation often used is 22/7, but a more accurate one would be 355/113. You can get closer and closer to pi with larger and larger numbers, but you will never truly be there. As such, I would just go with 22/7 before making matters too complicated. There are many answers you can go with, however. Here is a list of other examples.

13/4
16/5
19/6
22/7 - Most commonly used in school.
179/57
201/64
223/71
245/78
267/85
289/92
311/99
333/106
355/113