Question

Convert into vulgar fraction:
$5.\overline{234}$

Answer 1

Step: Convert into a vulgar fraction

Given: $5.\overline{234}$

$\Rightarrow 5.\overline{234}=\mathrm{5.234234...}$

Here, 2,3 and 4 are the three digits that are repeating in the decimal part.

$\Rightarrow 5.\overline{234}$

= $5+\frac{234-0}{999}$

= $5+\frac{234}{999}$

= $5+\frac{234÷9}{999÷9}$

= $5+\frac{26}{111}$

= $5\frac{26}{111}$

$\therefore 5.\overline{234}=5\frac{26}{111}$