Question

the value of $0.\overline{585}$ is equal to

• A. $\frac{589}{99}$
• B. $\frac{585}{999}$
• C. $\frac{999}{585}$
• D. None of these

Answer 1

Answer: (B)

$\frac{585}{999}$

$0.\overline{585}=\mathrm{0.585585585......}$

Let $x=\mathrm{0.585585585......}$ $\left(1\right)$

Multiply equation $1$ by $1000,$ we get

$1000x=\mathrm{585.585585585...........}$ $\left(2\right)$

Now subtracting equation $1)$ from equation $2),$ we get

$999x=585$

$\therefore x=\frac{585}{999}$