Problem Solving

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

I believe the logic is to find the recurring decimals and then pick one which is not a recurring decimal

Could someone explain the method to solve this?

One strategy is to do long division and hope that one of them eventually stops giving you decimals.

I hope someone else has a faster strategy.

Well, you would obviously get a answer to it with long division.

But i hope someone knows a strategy to solve this without consuming much time.

for these questions:
1) check whether you have 3 or 7 in the denominator
2) see if they cancel out with 3's or 7's in numerator
In case there are big numbers involved, check for bigger prime numbers too. But I am yet to see a question where u need to check for numbers >7


A. 10/189-denominator has 3*7*9. Numerator does not have those numbers. Numerator has 2*5. this will give you non terminating decimal


B. 15/196 - denominator has got 4*7*7. it will give non terminating
C. 16/225 -got 3 in the denominator
D. 25/144 got 3's in the denominator
E. 39/12 - got 3 int he denominator but also got a 3 in the numerator and they will cancel each other-
This is the answer E

The strategy here should be to see if you can get a 4 in the denominator after simplifying the fraction because division by 4 always gives a terminating decimal.

If you see answer choice E

39/12 = (13*3)/(4*3) = 13/4 = 3.25

Hence E.

I would suggest this link and read Ian Stewart's explaination.