# What is the best numerator and denominator couple to get the value of $\pi$?

I need to express the value of $\pi$ as numerator/denominator. What is the best pair considering that the numerator should be less than or equal to $2^{62}$? Or how to get this pair?

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– Qiaochu Yuan Feb 21 '11 at 12:04
I think $\frac{129988029236677443584}{41376474791582048256}$ is the closest fraction to $\pi$ with a numerator less than $2^{62}$.