We all know that 1/3 + 1/3 + 1/3 = 1, but 0.33 + 0.33 + 0.33 = 0.99. We're sufficiently used to decimal to know that 1/3 doesn't have a finite decimal representation. Decimal 1/10 doesn't have a finite binary representation, for the exact same reason that 1/3 doesn't have one in decimal — 3 is co-prime with 10, and 5 is co-prime with 2.
The only leaky abstraction here is our bias towards decimal. (Fun fact: "base 10" is meaningless, because every base calls itself base 10)
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We all know that 1/3 + 1/3 + 1/3 = 1, but 0.33 + 0.33 + 0.33 = 0.99. We're sufficiently used to decimal to know that 1/3 doesn't have a finite decimal representation. Decimal 1/10 doesn't have a finite binary representation, for the exact same reason that 1/3 doesn't have one in decimal — 3 is co-prime with 10, and 5 is co-prime with 2.
The only leaky abstraction here is our bias towards decimal. (Fun fact: "base 10" is meaningless, because every base calls itself base 10)
Maybe we should name the bases by the largest digit they have, so that we are using base 9 most of the time.