method float.as_integer_ratio() always ...

[Gribouillis]

those are less accurate approximations for Pi than the ratio i showed, which give the full precision that C double on x86 can represent, which is the type that Python uses.

If you want a better approximation of pi than the double precision constant math.pi, you can use a multiprecision library such as gmpy2 and/or a known numerical algorithm converging to pi. Many of the existing algorithms give rational approximations which could be passed to Fraction.limit_denominator(). You can also find easily millions of digits of pi directly on the web. A simple search points to a file suposedly from the MIT with 1 billion digits.