$355/113$ is a good fractional approximation of $\pi$, because we use six digits to produce seven correct digits of $\pi$.  

$$\frac{355}{113} = 3.1415929\ldots$$

Let $R$ be the ratio of the number of accurate digits produced to the number of digits used in the numerator and denominator, then  

$$R\left(\frac{355}{113}\right) = \frac 7{3+3} = 1.166666\ldots\,{}$$
Can anyone find a "better" fraction such that $R > 1.16666\ldots\,{}$.

**Added:** Probably, a similar question would also make sense over a base other than $10$.