Question

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

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

Answer 1

The correct option is C

$\frac{41111}{333000}$

Let $x=0.123\overline{456}$
Multiply the above equation with 1000 and 1000000, we get two equations;
$1000x=123.\overline{456}$ ........................(1)
$1000000x=123456.\overline{456}$ .....................(2)
Subtracting (1) from (2),
$1000000x-1000x=123456.\overline{456}-123.\overline{456}$
we get, $999000x=123333$
$x=\frac{123333}{999000}=\frac{41111}{333000}$