Question

$0.12\overline{3}$ can be expressed in rational form as

• A. $\frac{900}{111}$
• B. $\frac{111}{900}$
• C. $\frac{123}{10}$
• D. $\frac{121}{900}$

Answer 1

The correct option is B

$\frac{111}{900}$

Expressing the given number in rational form:

$0.12\overline{3}=0.12333....$

Let$x=0.12333\dots \dots$ ……(i)

Multiply (i) by $10$ on both sides, we get,

$\Rightarrow 10x=1.2333\dots ..$ ……(ii)

Subtracting equation (i) from (ii), we get

$$\begin{gathered} \Rightarrow 10x-x=1.2333-0.12333 \\ \Rightarrow 9x=1.11 \\ \Rightarrow x=\frac{1.11}{9} \\ \Rightarrow x=\frac{111}{900} \end{gathered}$$

Hence, option B is correct.