Solution
Let $$x =0.\overline{001}$$ be the first equation
$$1000x = 1000 \times 0.\overline001$$
= $$1.\overline{001}$$
Let $$1000x = 1.\overline{001}$$ be second equation
Subtracting equation 1 from 2
$$999x = 1$$
$$ x = \frac{1}{999}$$
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