It's phrased incredibly badly, but basically you can only write a fraction with a finite number of decimals if the denominator divides 10^k (for some k). This m

It's phrased incredibly badly, but basically you can only write a fraction with a finite number of decimals if the denominator divides 10^k (for some k). This means the denominator can't have prime factors other than 2 and 5 (which are the two prime factors of the base). This last statement isn't exactly trivial, but is reasonably easy to prove.