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I will choose E.
All other choices have a odd prime number in the denominator whereas E has only 2s.

Divide any number by an odd prime and it is going to be infinite. Anything with only 2s in denominator is finite; it either ends as a whole number or 0.5

Yes, that is what I thought. 225 is 15 square has 3 in it. 128 is 2^7 , so always give 0.5. Others are square which has 3 and 189 has 7 to make non-terminating.
Cheers.
S

Any number terminating in 5 shall give a terminating decimal, this theory is false , exactly for the exception yu mentioned, and 3 is not just the only combination.
_________________

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

Any number that either only contains: 2 or powers of 2 in the denominator OR 5 or powers of 5 OR mixture of powers of 2 and 5 (for example: 20 (2^2*5) ) would be eligible as a terminating decimal.

In case of your 2^n5^p denominator, what happens if numerator is a power of 3 ?? unterminated...

Hi Twixt

Which of power 3 in the numerator is giving you an unterminated result, apply my conclusion to any number contaning anything in the numerator, but the denomiator should only have powers of 2 or powers of 5 or a mixture of powers 2 and 5. It holds for all nos.

Linker, I am not sure i understand your theory : In case of your 2^n5^p denominator, what happens if numerator is a power of 3 ?? unterminated...

Yes. See examples below. I will take a common prime numerator, say 43.

43/32 -> terminating decimal -> Since it has only 2 as prime factor
43/625 -> terminating decimal -> Since it has only 5 as prime factor
43/50 -> terminating decimal -> Since it has only 2 and 5 as prime factors
43/150 -> not a terminating decimal -> Since it has 3 as a prime factor apart from 2 and 5
43/41 -> not a terminating decimal -> Since it does not have 2 or 5 as a prime factor.

I will rephrase my statement above: Any fraction with a denominator containing prime factors of only 2 and 5, will be have terminating decimal.