Question

The fractional value of $2.357$ is

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

Answer 1

The correct option is C

$\frac{2355}{999}$

(a) $\frac{2355}{999}$

$2.overling357=2.0+0.357+0.000357+0.000000357+....\infty$

$\Rightarrow 2.\overline{357}=2[\frac{357}{{10}^3}+\frac{357}{{10}^6}+\frac{357}{{10}^9}+....\infty ]$

$\Rightarrow 2.\overline{357}=2+\frac{\frac{357}{{10}^3}}{1-\frac{1}{{10}^3}}$

$\Rightarrow 2.\overline{357}=2+\frac{357}{999}\Rightarrow 2.\overline{357}=\frac{2355}{999}$