Question #f6a91

Jan 9, 2017

$\frac{895}{999}$

Explanation:

We require to obtain 2 equations with the same repeating part then subtract them to eliminate the repeating part.

$0. \overline{895} \text{ represents } 0.895895 \ldots .$

$\text{Let } x = 0. \textcolor{b l u e}{895} \rightarrow \left(A\right)$

To obtain the same repeating part after the decimal point we require to multiply by 1000

$\Rightarrow 1000 x = 895. \textcolor{b l u e}{895} \rightarrow \left(B\right)$

Subtracting (A) from (B) will eliminate the repeated fraction.

$\Rightarrow 999 x = 895 \leftarrow \text{ repeated fraction is eliminated}$

$\Rightarrow x = \frac{895}{999} \leftarrow \text{ in simplest form}$