jmc

Since the denominator of $\frac{9}{160}$ is $2^5\cdot 5$, we multiply numerator and denominator by $5^4$ to obtain $$\frac{9}{160}=\frac{9\cdot 5^4}{2^5\cdot 5\cdot 5^4}=\frac{9\cdot 625}{10^5}=\frac{5625}{10^5}=\mathrm{0.05625.}$$So, the digit in the hundredths place is $\boxed{5}$.