Question

How do you convert $0.8\overline{3}$ to a fraction?

Answer 1

Convert $0.8\overline{3}$ to a fraction:

Let $x=0.83333........\left(1\right)$

Multiply the above equation by $10$

$10x=10\times 0.83333.....$

$10x=8.3333........\left(2\right)$

Subtract equation $\left(1\right)$ from equation $\left(2\right)$

$$\begin{gathered} 10x-x=\left(8.33333.....\right)-\left(0.83333.....\right) \\ \Rightarrow 9x=7.5 \\ \Rightarrow x=\frac{7.5}{9}\left[\mathrm{Divide}\mathrm{by}9\mathrm{both}\mathrm{sides}\right] \\ \therefore x=\frac{5}{6} \end{gathered}$$

Hence, $0.8\overline{3}$ in terms of a fraction is $\frac{5}{6}$.