Question

The rational number which equals the number $2.\overline{357}$ with recurring decimal is

• A. $\frac{2355}{1001}$
• B. $\frac{2379}{997}$
• C. $\frac{2355}{999}$
• D. None of these

Answer 1

The correct option is C

$\frac{2355}{999}$

Compute the required number:

Let $x=2.\overline{357}$ $......\left(1\right)$

Multiply both sides by $1000$,

$\Rightarrow$ $1000x=2357.\overline{357}$$........\left(2\right)$

On subtracting $\left(1\right)$ from $\left(2\right)$

$\Rightarrow$$1000x-x=2357.\overline{357}-2.\overline{357}$

$\Rightarrow$ $999x=2355$

$\Rightarrow$ $x=\frac{2355}{999}$

Hence, option (C) is the correct option.