To what extent is it precise to evaluate Sympy enormous fractions (Rational)?
The size of SymPy Rationals is limited only by your available memory. If you want an approximate but memory bounded number, use a Float. You can convert a Rational into a Float with evalf.
I am using Sympy Rational in an algorithm and I am getting enormous factions. Numerator and Denominator grow up to 10000 digits. 
I would like to stop the algorithm as soon as the fractions become unevaluable. So the question is, what is the maximum magnitude I can allow for sympy.Rational?