Terminating Decimal

The rule is correct *if* your fraction is reduced. 3/30 is a terminating decimal despite having a 3 in the denominator - it is not, however, a reduced fraction. Yes, the answer would be B to the DS question Vittal asks above.

And... Happy New Year!

Yes, exactly right - so the following are all terminating decimals:

7/125
9/80
7/16

because, prime factorizing the denominators, 125 = 5^3, 80 = 2^4 * 5, and 16 = 2^4; we only have 2's and/or 5's. The following are *not* terminating:

4/75
11/30
17/175

because in each case, the fraction is reduced, and the denominator is divisible by a prime different from 2 or 5 (in the first two cases, the denominator is divisible by 3, and in the last case by 7).

Finally, the following might, at first glance, appear to represent *non*-terminating decimals, but they are terminating - you must reduce the fraction first:

11/275
81/216
49/280

If we reduce these fractions, we can see that we should get terminating decimals in each case: 11/275 = 1/25, 81/216 = 3/8 and 49/280 = 7/40.