Question

Express the following fractions as recurring decimals.

$\frac{1}{11}$

Answer 1

Converting the fraction into recurring decimal

Given, $\frac{1}{11}$

Let us express$\frac{1}{11}$as a decimal.

$$\begin{gathered} 11)1.00(0.090909..... \\ -99 \\ \_\_\_\_ \\ \times 100 \\ -99 \\ \_\_\_\_\_ \\ \times 100 \\ -99 \\ \_\_\_\_\_\_\_\_ \\ \times 100 \\ -99 \\ \_\_\_\_\_\_\_\_\_ \\ \times 1 \end{gathered}$$

Thus $\frac{1}{11}=0.090909......$

Here the digit $09$ is repeated in the quotient, so to convert it into a recurring decimal we put a bar over it.

So, $0.090909....$ is written as $0.\overline{09}$

Hence, $\frac{1}{11}=0.\overline{09}$