Question

Express the given decimal in the rational form: $4.\overline{7}$

Answer 1

Decimal = $4.\overline{7}=\mathrm{4.7777......}$

Let $x=\mathrm{4.7777......}$

$10x=\mathrm{47.777......}$

$10x-x=\mathrm{47.777......}-\mathrm{4.777......}$

$9x=43$

$x=\frac{43}{9}$ $p=43,q=9$ in $\frac{p}{q}$