[ycombobreaker]

This is pretty good for illustration to a layperson, thank you! Filling in a few other examples could be useful. For instance, why do 1/4 and 1/8 work in base-10?

I imagine you could create a table of the fractions 1/2, 1/3, ..., 1/10; prime factorization (e.g. 1/4 = 1/2 * 1/2), their decimal representation, their binary representation, and maybe for familiarity the sum-of-fractions represented by the binary representation. e.g. 0.101 meaning 1/2 + 1/8.