Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0 . \overline{35}$
Express the following in the form $\frac{p}{q},$ where $p$ and $q$ are integers and $q \neq 0 .$
$0 . \overline{35}$
$0 . \overline{35}$
Let, $x=0 . \overline{35}$
$\therefore x=0.3535 \ldots$ $....(1)$
Now, multiplying both the sides by $100 .$
$100 x=35.35 \ldots$ $\ldots \ldots(2)$
Subtract $(1)$ from $(2)$
$100 x=35.35 \ldots$
$\frac{-x=00.35\cdots}{99 x=35}$
$\therefore x=\frac{35}{99}$
Thus, $0 . \overline{35}=\frac{35}{99}$
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