Question

Express each of the following decimals as a rational number:
(ii) $0.\overline{35}$

Answer 1

Convert decimal into rational number.
$0.\overline{35}$
Let $x=0.\overline{35}$
Then,
$x=0.353535\dots \left(1\right)$
Here,
The number of digits recurring is $2$,
So, we multiply both sides of equation $\left(1\right)\text{by}100$
We get,
$100x=100\times 0.353535\dots$
$=35.3535\dots \left(2\right)$
On subtracting (1) from (2),
We get,
$99x=35$
$x=\frac{35}{99}$
Therefore,
$0.\overline{35}=\frac{35}{99}$