Question

Convert into vulgar fraction:
$0.4\overline{42}$

Answer 1

Step: Convert into a vulgar fraction

Given: $0.4\overline{42}$

$\Rightarrow 0.4\overline{42}=\mathrm{0.4424242...}$

Here, 4 and 2 are the two digits that are repeating in the decimal part.

$\Rightarrow 0.4\overline{42}$

$=\frac{442-4}{990}$

$=\frac{438}{990}$

$=\frac{438÷2}{990÷2}$

$=\frac{219}{445}$

$=\frac{219÷3}{445÷3}$

$=\frac{73}{165}$

$\therefore 0.4\overline{42}=\frac{73}{165}$