Question

State a general rule describing which fractions have decimal forms that terminate and

which have decimal forms that repeat.

Answer 1

factor the denominator of

the fraction (after it is reduced to lowest terms) into a product of
powers of prime numbers. If the prime factors are all 2 or 5, then the
decimal will terminate, otherwise it will repeat.

e.g. 1/125 = 1/5^3 = .008
3/20 = 3/(2^2*5) = .15

but 5/12 = 5/(4*3) = .416666...