Question

Express $2.4\overline{5}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$, is

Answer 1

Let $x=2.4\overline{5}$ .... (i)
since 5 is the only recuring part,
multiplying both sides with 10, We get
$10x=24.\overline{55}$ ... (ii)
Now subtracting (i) from (ii), we get
$9x=22.1$
on solving we get
$x=\frac{22.1}{9}$

$\therefore x=\frac{22.1}{9}$