jmc

Since a terminating decimal can be written in the form of $\frac{a}{10^b}$, where $a$ and $b$ are integers, we want to rewrite our fraction with a denominator of $10^b=2^b\cdot 5^b$. $$\frac{37}{80}=\frac{37}{2^4\cdot 5}\cdot \frac{5^3}{5^3}=\frac{37\cdot 5^3}{10^4}=\frac{4625}{10^4}=\boxed{0.4625}.$$