Question

Express the mixed recurring decimal $15.7\overline{32}$ in $\frac{p}{q}$ form.

Answer 1

Let, $x=15.7\overline{32}$

Since there is one digit after decimal and not under the bar, multiply by $10$ on both sides.

$10x=15.7\overline{32}\times 10$

$10x=157.\overline{32}$

$10x=157+0.\overline{32}$

$10x=157+\frac{32}{99}$

$10x=\frac{157\times 99+32}{99}=\frac{15575}{99}$

$x=\frac{15575}{990}$

This is in the form of $\frac{p}{q}$