Question
Express the following decimal as a rational number.$0.35$
✓
Answer
Let $x=0 . \overline{35}$
Then, $x=0.353535 \ldots$
Here, the number of digits recurring is $2,$
so we multiply both sides of the equation $(1)$ by $100 .$
$\therefore 100 x =100 \times 0.353535 \ldots$
$=35.3535 \ldots$
On subtracting $(1)$ from $(2),$ we get
$95 x=35 $
$\therefore x=\frac{35}{99} $
$\therefore 0.35=\frac{35}{99}$
Then, $x=0.353535 \ldots$
Here, the number of digits recurring is $2,$
so we multiply both sides of the equation $(1)$ by $100 .$
$\therefore 100 x =100 \times 0.353535 \ldots$
$=35.3535 \ldots$
On subtracting $(1)$ from $(2),$ we get
$95 x=35 $
$\therefore x=\frac{35}{99} $
$\therefore 0.35=\frac{35}{99}$
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