Question

$\frac{p}{q}$ form of the number $0.123\overline{456}$, where p and q are integers and $q\ne 0$, is ____

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

Answer 1

The correct option is C $\frac{41111}{333000}$

Given number is $0.123\overline{456}$
Let, $x=0.123\overline{456}$
Multiply both sides of $x$ by 1000
$\Rightarrow 1000x=\mathrm{123.456456......}$ ---(1)
Now, multiply both sides of $x$ by 1000000
$\Rightarrow 1000000x=\mathrm{123456.456456.......}$ ---(2)

Subtracting (1) from (2), we get
$1000000x-1000x=\left(\mathrm{123456.456456...}\right)-\left(\mathrm{123.456456..}\right)$
$\Rightarrow$$999000x=123333$
$\Rightarrow x=\frac{123333}{999000}=\frac{41111}{333000}$