Question

The rational number for recurring decimal $0.125125\dots$ is:

• A. $\frac{63}{487}$
• B. $\frac{119}{993}$
• C. $\frac{125}{999}$
• D. None of these

Answer 1

Answer: (C)

$\frac{125}{999}$

$\mathrm{0.125125....}=0.\overline{125}$

Let $x=0.\overline{125}$ ---- ( 1 )

Multiplying both sides by $1000$ we get,

$\Rightarrow$ $1000x=125.\overline{125}$ ---- ( 2 )

Subtracting ( 1 ) from ( 2 ) we get,

$\Rightarrow$ $1000x-x=125.\overline{125}-0.\overline{125}$

$\Rightarrow$ $999x=125$

$\therefore$ $x=\frac{125}{999}$

$\therefore$ Required rational number is $\frac{125}{999}.$