Your students should be able to figure out if a computation is exact or not, because they should understand binary representation of numbers.

Tell them that they can only store integer powers of 2 and their sums exactly. 2^0 == 1. 2^-2 == .25. Then say it's the same with base 10. 10^-1 == 0.1. 1/9 isn't a power of 10, you you can't have an exact representation.

They shouldn’t “memorize” this per se, but it should take them only a few seconds to work out in their head.