Question
Find the value of:$1. 32 - 0.91$
✓
Answer
Let $x =1 . \overline{32} \ldots( i )$
$\Rightarrow 100 x =132 . \overline{32} ...... (ii)$
Subtracting $(i)$ from $(ii),$
$99 x =131$
$\Rightarrow x =\frac{131}{99}$
Let $y =0.9 \overline{1}$
$ \Rightarrow 10 y =9 . \overline{1} \ldots . . . \text { (iii) }$
$\Rightarrow 100 y =9 . \overline{1} \quad \ldots \text { (iv) }$
Subtracting $(iii)$ from $(iv),$
$ 90 y=82$
$\Rightarrow y=\frac{82}{90}$
$=\frac{41}{45}$
$\therefore 1.32-0.91=x-y$
$=\frac{131}{99}-\frac{41}{45}$
$=\frac{131 \times 5-41 \times 11}{495}$
$=\frac{655-451}{495}$
$=\frac{204}{495}$
$=0.412$
$\Rightarrow 100 x =132 . \overline{32} ...... (ii)$
Subtracting $(i)$ from $(ii),$
$99 x =131$
$\Rightarrow x =\frac{131}{99}$
Let $y =0.9 \overline{1}$
$ \Rightarrow 10 y =9 . \overline{1} \ldots . . . \text { (iii) }$
$\Rightarrow 100 y =9 . \overline{1} \quad \ldots \text { (iv) }$
Subtracting $(iii)$ from $(iv),$
$ 90 y=82$
$\Rightarrow y=\frac{82}{90}$
$=\frac{41}{45}$
$\therefore 1.32-0.91=x-y$
$=\frac{131}{99}-\frac{41}{45}$
$=\frac{131 \times 5-41 \times 11}{495}$
$=\frac{655-451}{495}$
$=\frac{204}{495}$
$=0.412$
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