Question

Convert into vulgar fraction:
$0.2\overline{45}$

Answer 1

Step: Convert into a vulgar fraction

Given: $0.2\overline{45}$

$\Rightarrow 0.2\overline{45}=\mathrm{0.24545...}$

Here, 4 and 5 are the two digits that are repeating in the decimal part.

$\Rightarrow 0.2\overline{45}$

$=\frac{245-2}{990}$

$=\frac{243}{990}$

$=\frac{243÷9}{990÷9}$

$=\frac{27}{110}$

$\therefore 0.2\overline{45}=\frac{27}{110}$