# Rational approximation of pi

I found this problem intriguing: $355 / 113 = 3.14159292035398\ldots$ gives the approximation of $\pi$ in $7$ correct numbers, say $C(355/113)=7$, but it number of digits in numerator + number of digits in denominator is six, say $L(355/113)=6$. How many rationals $a/b$ there are such that $L(a/b)<C(a/b)$?