Question
Express the following decimal as a rational number.$0.7$
✓
Answer
Let $x=0.7$
Then, $x=0.7777 \ldots$
Here, the number of digits recurring is only $1,$
so we multiply both sides of the equation $(1)$ by $10 .$
$\therefore 10 x=10 \times 0.7777 \ldots . $
$=7.777 \ldots \ldots(2)$
On subtracting $(1)$ from $(2),$ we get
$9 x=7 $
$\therefore x=\frac{7}{9} $
$\therefore 0.7=\frac{7}{9}$
Then, $x=0.7777 \ldots$
Here, the number of digits recurring is only $1,$
so we multiply both sides of the equation $(1)$ by $10 .$
$\therefore 10 x=10 \times 0.7777 \ldots . $
$=7.777 \ldots \ldots(2)$
On subtracting $(1)$ from $(2),$ we get
$9 x=7 $
$\therefore x=\frac{7}{9} $
$\therefore 0.7=\frac{7}{9}$
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