Question

Express the following in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0:$

$\stackrel{\_\_\_\_\_}{0.001}$is $\frac{m}{999}$, then $m$ is equal to

Answer 1

Let $x$ be $\mathrm{0.001001001..}$
$=>1000x=\mathrm{1.001001...}$
$=>1000x=1+\mathrm{0.001001..}$
$=>1000x=1+x$
$=>1000x-x=1$
$=>999x=1$
$=>x=\frac{1}{999}$