Asked by A.W.
State a general rule describing which fractions have decimal forms that terminate and
which have decimal forms that repeat.
which have decimal forms that repeat.
Answers
Answered by
Reiny
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...
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...
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