Question

$0.\overline{001}$ when expressed in the form $\frac{p}{q}$ (p,q are integers, $q\ne 0$ ), is

• A. $\frac{1}{1000}$
• B. $\frac{1}{100}$
• C. $\frac{1}{1999}$
• D. $\frac{1}{999}$

Answer 1

The correct option is D

$\frac{1}{999}$

$0.\overline{001}$

Let x = $0.\overline{001}$ = 0.001001001.....

1000x = 1.001001001....

Subtracting,

999x = 1

$\Rightarrow$ x = $\frac{1}{999}$