Given the ancient Romans' achievements in the sciences, they must have understood the concept of quantities between zero and one. So how did they notate fractions? I/VII would get cumbersome and wouldn't aid in making calculations. Approximating pi would seem to be an impossibility.
-- Steve Gallagher, Spring Valley
I think you have the Romans confused with the Greeks, Steve. War, commerce, and bridge building were tops of the Romans' list. But even so, you're right about their lumpy number system. They handled fractions in a couple of ways. They might write it out, as in tres septimae, three-sevenths. They also had special symbols that represented fractions of known weights and measures. All very practical. As for calculating in Roman numerals, they used a version of the abacus. The values on the counting board were 1000, 100, 10, and 1. It took several hundred years for Europeans to get so exhausted with Xs and Vs and Ms that we finally adopted the sensible Indo-Arabic system we use now.