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
For a fraction to yield a terminating decimal, its denominator must be composed ONLY of 2's and/or 5's when the fraction is in its MOST REDUCED FORM.
Examples:
21/300 = 7/100 = 7/2²5² --> terminating, since the denominator is composted only of 2's and/or 5's.
2/60 = 1/30 = 1/(2*3*5) --> NOT terminating, since the denominator is NOT composed only of 2's and/or 5's.
Whenever a GMAT problem requires that all 5 answer choices be considered, the correct answer choice is likely to be near the BOTTOM.
Answer choice E: 39/128 = (3*13)/(2�).
Since the denominator is composed only of 2's and or 5's, the resulting decimal will be terminating.
The correct answer is
E.
Reasons to eliminate:
In any multiple of 3, the sum of the digits is a multiple of 3.
Thus, the denominators of A (189), C (225), and D (144) are all multiples of 3.
None of these answer choices can be further reduced.
Since the denominator in each case will not be composed only of 2's and/or 5's, none of these fractions will yield a terminating decimal.
Eliminate A, C and D.
Answer choice B: 15/196 = (3*5)/(2*2*7*7)
When this fraction is fully reduced, its denominator is NOT composed only of 2's and or 5's.
Thus, the resulting decimal will NOT be terminating.
Eliminate B.
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