Question

Convert the following into vulgar fractions: $0.\overline{56}$

Answer 1

$$\begin{gathered} 0.\overline{56}=0.5656..... \\ \mathrm{Let}\mathrm{x}=0.565656.......\left(1\right) \\ 100\mathrm{x}=56.565656..........\left(2\right) \\ \mathrm{Subtracting}\left(1\right)\mathrm{from}\left(2\right),\mathrm{we}\mathrm{get} \\ 99\mathrm{x}=56\Rightarrow \mathrm{x}=\frac{56}{99} \\ \mathrm{Hence},0.\overline{56}=\frac{56}{99} \end{gathered}$$