Question

Convert $\mathrm{0.18888.....}$ in $\frac{p}{q}$ form.

Answer 1

$\text{Let}x=0.1\overline{8}=\mathrm{0.18888...}...\left(1\right)$

Multiplying equation ( 1 ) with $10$

$\Rightarrow$ $10x=10\times \left(\mathrm{0.18888...}\right)$

$\Rightarrow$ $10x=\mathrm{1.8888....}$ $........\left(2\right)$

Subtrscting $\left(2\right)$ from $\left(1\right)$,

$10x-x=\mathrm{1.8888...}-\mathrm{0.18888...}$

$9x=\mathrm{1.7000...}$

$9x=1.7$

$x=\frac{1.7}{9}$

$\therefore$ $x=\frac{17}{90}$

$\therefore$ Required $\frac{p}{q}$ form is $\frac{17}{90}$