Question

Write the repeating decimal as a fraction or a mixed number

$2.\overline{36}$.

Answer 1

Given number: $2.\overline{36}$.

Let $\mathrm{x}=2.\overline{36}$

$\Rightarrow \mathrm{x}=2.363636...$ …(i)

Multiply by $10$ both sides

$\Rightarrow 100\times \mathrm{x}=100\times 2.363636...$

$\Rightarrow 100\mathrm{x}=236.363636...$ …(ii)

Subtract equation (i) from equation (ii)

$$\begin{gathered} \Rightarrow 100\mathrm{x}-\mathrm{x}=236.363636...-2.363636... \\ \Rightarrow 99\mathrm{x}=234 \\ \Rightarrow \mathrm{x}=\frac{234}{99} \\ \Rightarrow \mathrm{x}=\frac{26}{11} \end{gathered}$$

Hence, the fraction form of given decimal number is $\frac{26}{11}$.