Question

Express the given decimal in the $\frac{p}{q}$ form:$0.\overline{9}$

Answer 1

Decimal number = $0.\overline{9}=\mathrm{0.999.....}$

Let $x=0.\overline{9}=\mathrm{0.999....}$

$10x=\mathrm{9.9999.....}$

$10-x=\mathrm{9.999......}-\mathrm{0.999......}$

$9x=9$

$x=\frac{9}{9}=\frac{1}{1}$ $p=1q=1$ in $\frac{p}{q}$