jmc

To express the number $0.4\overline{5}$ as a fraction, we call it $x$ and subtract it from $10x$: \begin{array}{r r c r@{}l} &10x &=& 4&.55555\ldots \\ - &x &=& 0&.45555\ldots \\ \hline &9x &=& 4&.1 \end{array} This shows that $0.4\overline{5}=\frac{4.1}{9}=\boxed{\frac{41}{90}}$.