Question

Express $0.\overline{4}$ as a rational number in simplest form.

Answer 1

Let x be $0.\overline{4}$.

$x=0.\overline{4}$ .....(1)
Multiplying both sides by 10, we get
$10x=4.\overline{4}$ .....(2)

Subtracting (1) from (2), we get
$$\begin{gathered} 10x-x=4.\overline{4}-0.\overline{4} \\ \Rightarrow 9x=4 \\ \Rightarrow x=\frac{4}{9} \end{gathered}$$

Thus, simplest form of $0.\overline{4}$ as a rational number is $\frac{4}{9}$.