Question

Express the following as a rational number i.e. in the form $\frac{a}{b};$ where a, $b\in I$ and $b\ne 0.$

$0.\overline{572}$.

• A. $\frac{582}{999}$
• B. $\frac{572}{999}$
• C. $\frac{527}{999}$
• D. $\frac{562}{999}$

Answer 1

Answer: (B)

$\frac{572}{999}$

Let $x=0.\overline{572}$
$\therefore 1000x=572.\overline{572}$
Now subtract eq 2 and eq1
$\Rightarrow 999x=572$
$x=\frac{572}{999}$