Question

Express $\mathrm{1.323232........}+\mathrm{0.353535......}$ in the form of $\frac{p}{q}$ where $p$ and $q$ are integers and $q\ne 0$.

Answer 1

$\mathrm{1.323232.....}+\mathrm{0.3535.35....}$

Let $x=1.3232$ ………..$\left(1\right)$

$100x=132.3232$ ………..$\left(2\right)$

Equation $\left(2\right)$ - Equation $\left(1\right)$

$\Rightarrow 99x=131$

$\therefore x=\frac{131}{99}$

Let $y=0.353535$ ………..$\left(3\right)$

$100y=35.3535$ ……….$\left(4\right)$

$100y-y=35$

$y=35/99$

Now $x+y=\frac{131+35}{99}=\frac{166}{99}$.