Problem Solving

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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 powers of 2 and/or powers of 5 when the fraction is in its MOST REDUCED FORM.

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 each of these answer choices is in its most reduced form, and each has in its denominator something other than a power of 2 or a power of 5, none will yield a terminating decimal.
Eliminate A, C and D.

Answer choice B: 15/196 = (3*5)/(2*2*7*7)
Since in its most reduced form this fraction has in its denominator something other than a power of 2 or a power of 5, the resulting decimal will not be terminating.
Eliminate B.

The correct answer is E.

Answer choice E: 39/128 = (3*13)/(2^7).
Since in its most reduced form this fraction has in its denominator only a power of 2, the resulting decimal will be terminating.

Number Property: If the denominator of any fraction (in its lowest form) has its factors any prime number other than 2 and 5 then the value of the fraction will always be NON-TERMINATING

Out of the options given, Denominators are
189 = It Has factor 3 therefore NON-TERMINATING
196 = It Has factor 7 (square of 14) therefore NON-TERMINATING
225 = It Has factor 3 therefore NON-TERMINATING
144 = It Has factor 3 therefore NON-TERMINATING
128 = It Has factor 2 only (out of all primes) therefore TERMINATING

Answer: Option E