Express $0.4\overline5$ as a common fraction.
To convert a repeating decimal to a common fraction, I need to use a clever trick to eliminate the repeating part. Let me call the decimal $x$, so $x = 0.4\overline5$. If I multiply both sides by 10, I get $10x = 4.\overline5$. Now, if I subtract $x$ from $10x$, I get $9x = 4.\overline5 - 0.4\overline5$. But the right-hand side is just $4.1$, since the repeating parts cancel out. So, $9x = 4.1$, and dividing both sides by 9, I get $x = \frac{4.1}{9}$. To simplify this fraction, I can multiply the numerator and denominator by 10, which gives me $x = \frac{41}{90}$. This is the common fraction that is equivalent to $0.4\overline5$.

