Question 5
Let $S$ be the set of all rational numbers $r,$ $0\lt r\lt1,$ that have a repeating decimal expansion in the form $$
0.abcabcabc\ldots=0.\overline{abc},
$$ where the digits $a,$ $b,$ and $c$ are not necessarily distinct. To write the elements of $S$ as fractions in lowest terms, how many different numerators are required?
0.abcabcabc\ldots=0.\overline{abc},
$$ where the digits $a,$ $b,$ and $c$ are not necessarily distinct. To write the elements of $S$ as fractions in lowest terms, how many different numerators are required?