That makes perfect sense, athough I won't remember it! Don't know why that was not taught at school or college, surely simpler than calculus. Probably should fit in about the same time as logs and trigonometry.
gfvalvo:
For a fraction to be represented exactly using a finite number of digits to the right of the Radix Point, its denominator must be representable as the product of powers of the radix's prime factors.
Aww, I was hoping he'd work it out for himself. Any finite binary fraction is a finite decimal one, because 10 is divisible by 2. But 2 is not divisible by 5, so it doesn't work the other way around.