Question

Express $0.2\overline{52}$ in the form $\frac{p}{q}$ where $p$ and $q$ are integers, $q\ne 0$.

Answer 1

Let, $x=0.2\overline{52}$,

then, $10x=2.\overline{52}$..........(1)

$=2.52\overline{52}$

and $1000x=252.\overline{52}$...........(2)

Now, subtracting (1) from (2) we get,

$990x=250$

$x=\frac{250}{990}=\frac{25}{99}$

which is in the form of the $\frac{p}{q}$