Question

Convert $0.\overline{45}$ in the form of $\frac{p}{q}\left(p,q\in Z,q\ne 0\right)$

Answer 1

Let $x=0.\overline{45}$

$x=0.454545454545$ . . . (1)

Multiply equation (1) with $100$

$100x=45.4545454545$ . . . (2)

Subtract equation (2) from (1)

$100x-x=\mathrm{45.4545...}-\mathrm{0.4545...}$

$\Rightarrow 99x=$ 45

$\Rightarrow 11x=5$

$\Rightarrow x=\frac{5}{11}$