Question

Convert the following into vulgar fractions: $0.\overline{2}$

Answer 1

$$\begin{gathered} 0.\overline{2}=0.2222.... \\ \mathrm{Let}\mathrm{x}=0.2222...........\left(1\right) \\ 10\mathrm{x}=2.222...........\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ 9\mathrm{x}=2\Rightarrow \mathrm{x}=\frac{2}{9} \\ \mathrm{Hence},0.\overline{2}=\frac{2}{9} \end{gathered}$$