Question

How do you convert $0.83$ ($3$repeating) to a fraction?

Answer 1

Convert into fraction.

Given, $\mathrm{x}=0.8333...$

$\Rightarrow$ $\mathrm{x}=0.8\overline{3}$

$\Rightarrow$ $10\mathrm{x}=8.\overline{3}$ $...\left(\mathrm{i}\right)$

$\Rightarrow$$100\mathrm{x}=83.\overline{3}$ $...\left(\mathrm{ii}\right)$

Subtract $\left(\mathrm{i}\right)$ from $\left(\mathrm{ii}\right)$, we get;

$100\mathrm{x}-10\mathrm{x}=83.\overline{3}-8.\overline{3}$

$\Rightarrow$ $90\mathrm{x}=75$

$\Rightarrow$ $\mathrm{x}=\frac{75}{90}$

$\Rightarrow$ $\mathrm{x}=\frac{5}{6}$

Hence, conversion of $0.83$ ($3$repeating) to a fraction is $\frac{5}{6}$.