Find the fraction that equals $0.\overline{4}$.
We have \[0.\overline{4} = \frac{4}{10} + \frac{4}{100} + \frac{4}{1000} + \cdots.\]This infinite geometric series has first term $4/10=2/5$ and common ratio $1/10$, so we have \[0.\overline{4} = \frac{2/5}{1-1/10} = \boxed{\frac{4}{9}}.\]
\frac{4}{9}
Level 2
Algebra
Problem: Find the fraction that equals $0.\overline{4}$.
Solution:<|START_OF_LATENT|><|PRIOR_PREFIX|>To convert the repeating decimal $0.\overline{4}$ into a fraction, let \( x = 0.\overline{4} \). This means that \( x = 0.4444\ldots \). To eliminate the repeating part, multiply both sides of the equation by 10: 

\( 10x = 4.4444\ldots \).

Now, we have two equations:

1. \( x = 0.4444\ldots \)
2. \( 10x = 4.4444\ldots \)

Next, subtract the first equation from the second:

\( 10x - x = 4.4444\ldots - 0.4444\ldots \).

This simplifies to:

\( 9x = 4 \).

To isolate \( x \), divide both sides by 9:

\( x = \frac{4}{9} \).

Thus, the fraction that equals \( 0.\overline{4} \) is \( \frac{4}{9} \).<|END_OF_LATENT|> The final answer is $\frac{4}{9}$.