Question

Express the following recurring decimals as fractions.

$0.\overline{17}$

Answer 1

Expressing the recurring decimal as fraction

Given, $0.\overline{17}$

Let $x=0.\overline{17}=0.171717.....\left(i\right)$

Multiplying both the sides by $100$ we get

$100x=17.1717....\left(ii\right)$

Subtracting $\left(i\right)$ from $\left(ii\right)$ we get

$$\begin{gathered} 100x-x=17.1717....-0.1717.... \\ \Rightarrow 99x=17 \\ \Rightarrow x=\frac{17}{99} \end{gathered}$$

Hence, $0.\overline{17}=\frac{17}{99}$