One Hundred from Nine Digits

Using each of the digits $1$ to $9$ exactly once, and only plus signs and a fraction bar, write an expression equal to $100$.

Solution

A neat one is $$91 + \frac{5742}{638} = 91 + 9 = 100,$$ in which the digits $9, 1, 5, 7, 4, 2, 6, 3, 8$ are precisely $1$ to $9$, each used once. There are several others in the same spirit, for instance $$81 + \frac{7524}{396} = 81 + 19 = 100 \qquad \text{and} \qquad 82 + \frac{3546}{197} = 82 + 18 = 100,$$ each again using every digit once. The knack is to pick the whole-number part, see how much is missing from $100$, and then arrange the leftover digits into a fraction equal to that shortfall.