The numerator and denominator get automatically reduced to lowest terms (just like you learned in elementary school, so 15/100 becomes 3/20) internally by every implementation I know of. This comes at a performance cost for every operation, but it helps keeping the numerator and denominator from blowing up.
>not sure how rounding works -- or even if they do rounding at all
They do not. The point of a Rational type is to keep precise values, so it's up to the programmer to decide when and how values are rounded.
>"arbitrary precision floating point" type like ruby's BigDecimal
Not sure how Ruby implements BigDecimal, but Java internally represents it as an BigInteger of digits, and a second integer that represents where in the number the decimal point should go. This means that BigDecimal still can't truly represent a value such as 1/3, since you can't have an infinite amount of 3's, but a Rational can.
>I'm not actually sure what domains rational data types are good for.
I'll be honest and say I've never had to use them either, but it's nice to know they exist. The intended use case is when you need to perform calculations and maintain as much precision and accuracy as possible in the intermediate values and such accuracy is more important than speed.