> you can't write ... and get something that works.

That's taking things a bit far, isn't it? Sure, you can't exactly express 0.1 as a double - but you can get many things that work really well using the approximation.

What I meant to say was, "you can't expect something with a terminating representation in base 10 to always have a terminating representation in base 2". When you play with these cases in base 10, it builds intuition that can be applied to base 2 math.