Let \mathcal{S} be the set of real numbers that can be represented as repeating decimals of the form 0 . \overline{a b c} where a, b, c are distinct digits. Find the sum of the elements of \mathcal{S}.
Let \mathcal{S} be the set of real numbers that can be represented as repeating decimals of the form 0 . \overline{a b c} where a, b, c are distinct digits. Find the sum of the elements of \mathcal{S}.