Problem Solving

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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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

A fraction will convert to a terminating decimal when the denominator of the simplified fraction contains only 5's, only 2's, or both 5's and 2's.

Since 231/660 = 77/220 = 7/20, and the denominator 20 = 2^2 x 5, we see that 231/660 will terminate.

Answer: D