Question

Write the repeating decimal as a fraction or a mixed number

$0.\overline{4}$.

Answer 1

Given number: $0.\overline{4}$.

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

$\Rightarrow \mathrm{x}=0.444...$ …(i)

Multiply by $10$ both sides

$\Rightarrow 10\times \mathrm{x}=10\times 0.444...$

$\Rightarrow 10\mathrm{x}=4.444...$ …(ii)

Subtract equation (i) from equation (ii)

$$\begin{gathered} \Rightarrow 10\mathrm{x}-\mathrm{x}=4.444...-0.444... \\ \Rightarrow 9\mathrm{x}=4 \\ \Rightarrow \mathrm{x}=\frac{9}{4} \end{gathered}$$

Hence, the fraction form of given decimal number is $\frac{4}{9}$.