Question

Convert each of the following recuring decimals in to a vulgar fraction.
$0.1\overline{8}$

Answer 1

Let $x=0.1\overline{8}$

Now, $10x=1.\overline{8}$

or, $10x-1=.\overline{8}$ .....(1).

$10x-1=.888888......$

Again,

$(10x-1)\times 10=8+.\overline{8}$

or, $(10x-1)\times 10=8+(10x-1)$ [ Using (1)]

or, $9(10x-1)=8$

or, $10x-1=\frac{8}{9}$

or, $10x=\frac{17}{9}$

or, $x=\frac{17}{90}$.