Question

How do we represent $0.123\overline{456}$ in fraction?

• A. $\frac{41111}{333000}$
• B. $\frac{41111}{999000}$
• C. $\frac{3333}{99000}$
• D. $\frac{12333}{99000}$

Answer 1

The correct option is A

$\frac{41111}{333000}$

Let $x=0.123\overline{456}$

Multiplying the above equation with 1000 and 1000000, we get the following equations:
$1000x=123.\overline{456}$ ........................(1)
$1000000x=123456.\overline{456}$ .....................(2)

On subtracting (1) from (2), we get,
$1000000x-1000x=123456.\overline{456}-123.\overline{456}$
$\Rightarrow$ $999000x=123333$
$\Rightarrow$ $x=\frac{123333}{999000}$
$\Rightarrow$ $x=\frac{41111}{333000}$