method float.as_integer_ratio() always ...

[Gribouillis]

This approximate is also given by the Fraction module

>>> from fractions import Fraction as F
>>> y = F(884279719003555,281474976710656)
>>> y.limit_denominator(100000000)
Fraction(245850922, 78256779)

The purpose of float.as_integer_ratio() is to give an integer ratio that is exactly equal to the real number stored in memory (which is not pi but an approximation of pi). It is a different problem from approximating pi with shorter fractions. The IEEE754 format indeed implies that the actual denominator is a power of two.

Note that for most floating numbers, you cannot expect a significant reduction of the size of the integers by doing this because the global number of bits needed to distinguish these numbers is fixed.