BTGmoderatorDC wrote:Which of the following fractions will terminate when expressed as a decimal?
(A) 1/259
(B) 27/101
(C) 100/27
(D) 231/660
(E) 1/11
OA D
Source: Manhattan Prep
A fraction when reduced such that the numerator and the denominator are co-prime to each other and its denominator has factors of only 2 and 5 will terminate.
For example, a fraction 21/750 will terminate since 21/750 can be reduced to 7/250, where 7 and 250 are co-prime and the denominator 250 can be factorized as 2*5^5.
Out of the given five options, only option D will terminate since 231/660 will reduce to (7*33) / (20*33) = 7/20. We see that 7 and 20 are co-prime to each other and the dominator 20 = 2^2*5.
The correct answer:
D
Hope this helps!
-Jay
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