Question

Express $1.\overline{62}$ in the $\frac{p}{q}$ form where $q\ne 0;p,q$ are integers

Answer 1

given number is$1.\overline{62}$

Let $x=\mathrm{1.626262.......}$...........(1)

Multiply (1) by 100 we get

$100x=162.626262$..............(2)

Substruct (2) by (1) we get

$99x=161$

$\Rightarrow x=\frac{161}{99}$

$\therefore 1.\overline{62}=\frac{161}{99}$