Question

Express $7.\overline{85}$ into fraction ?

• A. $\frac{778}{99}$
• B. $\frac{785}{1000}$
• C. $7\frac{85}{99}$
• D. 9$\frac{75}{99}$

Answer 1

Answer: (A), (C)

$7\frac{85}{99}$

Let $7.\overline{85}=7.858585.....=M$ ............(1)
Multiplying both side by 100 we get,
$\Rightarrow \mathrm{785.85858585....}=100M$ .........(2)
Substracting equation (1) from (2) we get,
$\Rightarrow \mathrm{785.8585....}-\mathrm{7.8585....}=100M-M$
$\Rightarrow 778=99M$
$\Rightarrow M=\frac{778}{99}$
Converting it into mixed fraction we get,
$\Rightarrow M=7\frac{85}{99}$.