LUANDATO wrote:Which of the following does NOT have a decimal equivalent that is a terminating decimal?

A. 1/2^25
B. 5^3/2^7
C. 3^8/6^10
D. 3^9/6^7
E. 6^8/10^10

The OA is C.

I'm confused with this PS question. Please, can any expert assist me with it? Thanks in advanced.

Important rule: a fraction can expressed as terminating decimal if, when reduced to simplest form, the denominator can be expressed as 2^n * 5^m, where n and m are non-negative integers.

Out another, if, when a fraction is reduced to its simplest form, there is something in the denominator other than 2's or 5's, we know this fraction is non-terminating.

Right away, we can see that A, B, and E are terminating. The denominators in A and B are composed solely of 2's, and in E, we have 10^10 = (2*5)^10, and thus consists solely of 2's and 5's.

D) (3^9)/(6^7) = (3^9)/(2^7 * 3^7) = (3^2)/(2^7). The denominator consists solely of 2's and so the decimal will terminate.

That leaves us with C. (There's really no need to evaluate it, as we already know that A, B, D, and E are all terminating, but if you want to confirm...
(3^8)/(6^10) = 3^8/(3^10 * 2^10) = 1/(3^2 * 2^10). Notice the 3^2 in the denominator. Because we have a prime base aside from 2 and 5 in the reduced fraction, we know that this decimal will not terminate.