Question

How do we represent $0.123\overline{456}$ in $\frac{p}{q}$ form?

• 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 $x=0.123\overline{456}$
$1000x=123.\overline{456}$ ... (i)
$1000000x=123456.\overline{456}$ ... (ii)

Subtract (i) from (ii):
$\Rightarrow 999000x=123333$
$\Rightarrow x=\frac{123333}{999000}=\frac{41111}{333000}$