Re "base-10 rational numbers that can’t be specified exactly as a base-2 floating point number?" All floating point representations purport to encode non-special values (such as NaNs) as rational numbers. Most of them (counting by usage) can only represent rational numbers with a power of 2 in the denominator. Hence, all negative powers of 10 cannot be represented, as they would have a (maybe repeated) factor of 5 in the denominator. There have been machines and software that represented "floating point" with the exponent understood to be and treated as a power of 10. They can represent common decimal fractions (such as hundredths) exactly. For some reason, ever since I stopped picking up pennies laying in public places, (at least the dirty ones), I have been amused at all the falderal about representing cents exactly. If that really matters, why not just represent cents instead of some multiple considered less "fundamental"? (Yes, yes, it is important for accounting, somehow. As if that can be exact.)