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

Question

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

What is the easier way of solving this problem without a calculator. Thanks.

Answer 1

Hint:

If the denominator has factors of only 2 or 5 then you will get a terminating decimal.

Notice:

1/2 = 0.5 (good)

1/3 = 0.3333.... (bad)

1/4 = 0.25 (good)

1/5 = 0.2 (good)

1/6 = 0.16666... (bad)

1/7 = 0.142857142857... (bad)

1/8 = 0.125 (good)

1/9 = 0.11111... (bad)

1/10 = 0.1 (good)

1/11 = 0.0909... (bad)

etc.

189 --> 1 + 8 + 9 = 18 (multiple of 3)

196 --> 2 x 2 x 7 x 7 (multiple of 7)

225 --> 2 + 2 + 5 = 9 (multiple of 3)

144 --> 1 + 1 + 4 = 6 (multiple of 3)

128 --> 2 x 2 x 2 x 2 x 2 x 2 x 2

128 has only factors of 2 (or 5).

Answer:

E.  39/128

Answer 2

D

SQRT25/SQRT144

5/12

Answer 3

E