Question

The rational number of the form $\frac{p}{q},q\ne 0$ , $p$ and $q$ are positive integers, which represents $0.1\overline{34}$ i.e., $\left(\mathrm{0.1343434......}\right)$ is

• A. $\frac{134}{999}$
• B. $\frac{134}{990}$
• C. $\frac{133}{999}$
• D. $\frac{133}{990}$

Answer 1

Answer: (D)

$(\frac{133}{990})$

Let $x=0.1343434\dots$ ---------(i)
Multiply $10$ on both sides, we get
$10x=1.343434\dots$ ----------(ii)
Similar way, multiply $100$ on both sides, we get
$1000x=\mathrm{134.3434....}$

Subtracting equation(ii) from equation(iii), we get
$1000x-10x=(134.3434\dots )-(1.343434\dots )$
$990x=133$
$x=\frac{133}{990}$

Hence, the required rational number is $\frac{133}{990}$