Question

Convert the following into vulgar fractions: $0.\overline{4}$

Answer 1

$$\begin{gathered} 0.\overline{4}=0.4444..... \\ \mathrm{Let}\mathrm{x}=0.4444........\left(1\right) \\ 10\mathrm{x}=4.444...........\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ 9\mathrm{x}=4\Rightarrow \mathrm{x}=\frac{4}{9} \\ \mathrm{Hence},0.\overline{4}=\frac{4}{9} \end{gathered}$$