Question
Find the value of:$2.12 - 0.45$
✓
Answer
Let $x=2 . \overline{12} \ldots(i) $
$\Rightarrow 100 x=212.12 ........(ii)$
Subtracting $(i)$ from $(ii),$
$99 x =210 $
$\Rightarrow x =\frac{210}{99} $
$=\frac{70}{33} $
Let $y =0.4 \overline{5} $
$\Rightarrow 10 y =4 . \overline{5} ......(iii) $
$\Rightarrow 100 y =45 . \overline{5} .......(iv)$
Subtracting $(iii)$ from $(iv),$
$90 y =41 $
$\Rightarrow y =\frac{41}{90} $
$\therefore 2 . \overline{12}-0.4 \overline{5}= x - y $
$=\frac{70}{33}-\frac{41}{90} $
$=\frac{70 \times 30-41 \times 11}{990} $
$=\frac{2100-451}{990} $
$=\frac{1649}{9 \underline{90}} $
$=1.665$
$\Rightarrow 100 x=212.12 ........(ii)$
Subtracting $(i)$ from $(ii),$
$99 x =210 $
$\Rightarrow x =\frac{210}{99} $
$=\frac{70}{33} $
Let $y =0.4 \overline{5} $
$\Rightarrow 10 y =4 . \overline{5} ......(iii) $
$\Rightarrow 100 y =45 . \overline{5} .......(iv)$
Subtracting $(iii)$ from $(iv),$
$90 y =41 $
$\Rightarrow y =\frac{41}{90} $
$\therefore 2 . \overline{12}-0.4 \overline{5}= x - y $
$=\frac{70}{33}-\frac{41}{90} $
$=\frac{70 \times 30-41 \times 11}{990} $
$=\frac{2100-451}{990} $
$=\frac{1649}{9 \underline{90}} $
$=1.665$
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