Question

Find the value of given mathematical expression
$1.02\overline{32}$$\times \frac{99}{1013}$

• A. $\frac{1}{10}$
• B. $\frac{1013}{990}$
• C. $\frac{10}{1}$
• D. None of the above

Answer 1

The correct option is A $\frac{1}{10}$

Let $1.02\overline{32}=1.02323232.....=M$ .........(1)
Multiplying both side by 100 we get,
$\Rightarrow \mathrm{102.3232....}=100M$ .........(2)
Substracting equation (1) from equation (2) we get,
$\Rightarrow \mathrm{102.3232...}-\mathrm{1.023232...}=100M-M$
$\Rightarrow 101.3=99M$
$\Rightarrow M=\frac{101.3}{99}$
Removing decimal we get,
$\Rightarrow M=\frac{1013}{990}=$$1.02\overline{32}$

$1.02\overline{32}\times \frac{99}{1013}$$=\frac{1013}{990}\times \frac{99}{1013}=\frac{1}{10}$