Question

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

• A. $\frac{2355}{1001}$
• B. $\frac{2370}{999}$
• C. $\frac{2355}{999}$
• D. $\frac{2359}{991}$

Answer 1

The correct option is C $\frac{2355}{999}$

Let the number given be $x=\mathrm{2.357357.....}$
Now multiplying both sides by ${10}^3$
$x\times {10}^3=\mathrm{2357.357357....}$
Now subtracting the two equations we get,
$999x=2355$ (decimal part will get cancelled in subtraction!)
$\therefore x=\frac{2355}{999}$