Question

The number $1.\overline{27}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$, is:

• A. a) $\frac{14}{11}$
• B. b) $\frac{14}{9}$
• C. c) $\frac{14}{15}$
• D. d) $\frac{14}{13}$

Answer 1

The correct option is A

a) $\frac{14}{11}$

Explanation for correct option:

Option a): $\frac{14}{11}$

Let $x=1.\overline{27}$

$\therefore$ $x=1.272727.......$ $\left(1\right)$

Multiplying each side by 100 in $\left(1\right)$, we get,

$100x=127.2727......\left(2\right)$

Subtracting $\left(1\right)$ from $\left(2\right)$,

$99x=126$

$$\begin{gathered} x=\frac{126}{99} \\ =\frac{14}{11} \end{gathered}$$

Therefore, the number $1.\overline{27}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$ is $\frac{14}{11}$.

Explanation for incorrect options:

Since the number $1.\overline{27}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$, is $\frac{14}{11}$, options $b),c)\&d)$ that is $\frac{14}{9}$,$\frac{14}{15}$$\&\frac{14}{13}$ are incorrect answers.

Hence, option $\left(a\right)$ is the correct answer.