KöMaL 2024 C1837

The ancient Greeks were already familiar with the fact that $\pi\approx 3.1416$ can be approximated with the fraction $22/7 \approx 3.1429$. How many pairs of positive integers $(a;b)$ satisfy the following properties: $1<b<100$ and the decimal form of $\frac{a}{b}$ starts as $3.14$?