Question

0.12333... 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

$\frac{111}{900}$

Let x = 0.12333
Multiplying by 100 on both sides, we get
100x = 12.333... (i)
Multiplying by 1000 on both sides, we get
1000x = 123.33...
Subtracting (i) from (ii), we get,

$900x=\mathrm{123.33.....}-\mathrm{12.333.....}$
$=111$

$\Rightarrow x=\frac{111}{900}$