Question

How to convert $0.2\overline{54}$ into fractional form.

Answer 1

Let $x=$ $0.2\overline{54}$ . Then,

$x=\mathrm{0.2545454...}$ .......(1)

Therefore, $10x=\mathrm{2.545454...}$ ........(2)

And, $1000x=\mathrm{254.545454...}$ ........(3)

On subtracting (2) from (3), we get

$990x=252⟹x=\frac{252}{990}=\frac{126}{495}=\frac{12}{165}=\frac{14}{55}$.