smc

Multiplying by $100$ gives $100F=\mathrm{48.181818...}$. Subtracting the first equation from the second gives $99F=47.7$, and all the other repeating parts cancel out. This gives $F=\frac{47.7}{99}=\frac{477}{990}=\frac{159}{330}=\frac{53}{110}$. Subtracting the numerator from the denominator gives $\boxed{57}$.