Question

Express $0.\overline{4}$ in the form$\frac{p}{q}$.

Answer 1

Represent given number in fraction form

Let $x=0.\overline{4}$
$0.\overline{4}=0.4444....$

So,$x=0.444...----\left(1\right)$

Multiplying both sides by 10.
$10x=4.444....----\left(2\right)$
Subtracting (1) from (2),
$$\begin{gathered} 10x-x=4.444....-0.444.... \\ 9x=4 \\ x=\frac{4}{9} \end{gathered}$$
Hence, $0.\overline{4}=\frac{4}{9}$