Question

Express $0.\overline{5}$ in the $\frac{p}{q}$ form

Answer 1

Let $x=0.\overline{5}=0.55555$...................(1)

Multiply by 10 we get

$10x=5.5555$........................................(2)

Substituting (1) and (2) we get

$10x-x=5.5555-0.5555$

$\Rightarrow 9x=5$

$\Rightarrow x=\frac{5}{9}$

Then $0.\overline{5}=\frac{5}{9}$