Question

Question 3 (iii)
Express $0.\overline{001}$ in the form $\frac{p}{q}$, where p and q are integers and $q\ne 0$.

Answer 1

$0.\overline{001}$= 0.001001...
Let x = 0.001001...
$\Rightarrow$ 1000x = 1.001001… [Since, there are three repeating decimal digits, so multiply x with 1000.]
$\Rightarrow$ 1000x = 1+ 0.001001
$\Rightarrow$ 1000x = 1 + x
$\Rightarrow$ 999x = 1
$\Rightarrow x=\frac{1}{999}$