Question

What is $1.6$ repeating as a fraction?

Answer 1

To convert into fraction:

Let,

$x=1.\overline{6}=1.666666666...$. (1)

Multiply by $10$ on both side.

$10x=16.\overline{6}...\left(2\right)$

Subtract equation (2)-equation (1)

$$\begin{gathered} 10x-x=16.\overline{6}-1.\overline{6} \\ \Rightarrow 9x=15 \\ \Rightarrow x=\frac{15}{9}=\frac{5}{3}=1\frac{2}{3} \end{gathered}$$

Hence, the fraction of $1.\overline{6}$ is $\mathbf{1}\frac{\mathbf{2}}{\mathbf{3}}$.