Which one of the following expressions is a terminating decimal? (A) 1

Question

Which one of the following expressions is a terminating decimal?

(A)  \frac{1 }{ (12^3) (5^5)}

(B)  \frac{1 }{ (4^7) (6^3)}

(C)  \frac{1 }{ (2^9) (7^5)}

(D)  \frac{1 }{ (4^4) (5^5)}

(E)  \frac{1 }{ (15^6) (2^8)}

CrackverbalGMAT · Answer

A terminating decimal is one, where the decimals don't go on forever.

There are 2 types of Non Terminating decimals (a) Recurring and (b) Non Recurring.

We get these types of decimals if the denominator contains a prime number or it's multiples. The only exceptions are 2 and 5.

For eg. 1/3 = 0.333.., 1/6 has 2 and 3 in the denominator. Since it has a 3, it is a non terminating decimal = 0.16666..

If the denominator contains only 2's, 5's or multiples of 10 (2x5), then it is a terminating decimal.

Looking at the Options, we see

Option A:    12^3 = (3 * 4)^3 . Therefore this is a non terminating decimal.

Option B:    6^3 = (2 * 3)^3 . Therefore this is a non terminating decimal.

Option C:   It has a 7 in the denominator. Therefore this is a non terminating decimal.

Option E:    15^3 = (5 * 3)^3 . Therefore this is a non terminating decimal.

Option D:   Has only prime numbers 2 and 5 in the denominator. Therefore this is a terminating decimal.

Option D

Arun Kumar

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