Question

Express $1.\overline{35}$ in $\frac{p}{q}$ from.

Answer 1

Let $a=\mathrm{1.3535....}$
$10a=\mathrm{13.53535....}$ ------(1)
$1000a=\mathrm{1353.53535...}$ ------(2)

On subtracting equation 1 from 2, we get
$990a=1340$
$=>a=\frac{1340}{990}.$ which is in $\frac{p}{q}$ form.
Hence, this is the answer.