decimal

[GmatKiss]

Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/ 128

[Anurag@Gurome]

Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/ 128

Here is a shortcut method: A fraction in lowest terms with a prime denominator other than 2 or 5 always produces a repeating decimal.

Thus if the denominator of a fraction after canceling all the common factors with the numerator contains any prime other than 2 or 5 in their prime factorization, then the fraction does not have a decimal equivalent that is a terminating decimal.

A] 10/189 --> 189 contains 3, 10 doesn't => Repeating Decimal
B] 15/196 --> 196 contains 7, 15 doesn't => Repeating Decimal
C] 16/225 --> 225 contains 3, 16 doesn't => Repeating Decimal
D] 25/144 --> 144 contains 3, 25 doesn't => Repeating Decimal
E] 39/128 --> 128 contains 2 only => Terminating Decimal


The correct answer is E.

[ronnie1985]

any fraction with denominators having powers of 2 and 5 only are terminating decimals

128 = 2^7
(E) is answer