Which of the following fractions will terminate when express

Question

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

Bunuel · Accepted Answer

THEORY: Reduced fraction \frac{a}{b} (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only b (denominator) is of the form 2^n5^m , where m and n are non-negative integers. For example: \frac{7}{250} is a terminating decimal 0.028 , as 250 (denominator) equals to 2*5^3 . Fraction \frac{3}{30} is also a terminating decimal, as \frac{3}{30}=\frac{1}{10} and denominator 10=2*5 . Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not. For example \frac{x}{2^n5^m} , (where x, n and m are integers) will always be the terminating decimal. We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \frac{6}{15} has 3 as prime in denominator and we need to know if it can be reduced. BACK TO THE QUESTION: If you check each option you get that only 231/660 will terminate: 231/660 = 7/20 = 7/(2^2*5). Answer: D. Questions testing this concept: does-the-decimal-equivalent-of-p-q-where-p-and-q-are-89566.html any-decimal-that-has-only-a-finite-number-of-nonzero-digits-101964.html if-a-b-c-d-and-e-are-integers-and-p-2-a3-b-and-q-2-c3-d5-e-is-p-q-a-terminating-decimal-125789.html 700-question-94641.html is-r-s2-is-a-terminating-decimal-91360.html pl-explain-89566.html which-of-the-following-fractions-88937.html Hope it helps.

PareshGmat · Answer

\frac{231}{660} = \frac{21}{60} = \frac{7}{20} = \frac{35}{100} = 0.35

No other option can be simplified further to bring  10^n  in the denominator

Answer = D

ScottTargetTestPrep · Answer

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

IanStewart · Answer

Of course one can prove that 231/660 is a terminating decimal by reducing the fraction, but there's no need to do even that. We know we only ever get a terminating decimal when we can reduce a fraction to something with no primes other than 2 and 5 in the denominator. The denominators of answers A, B, C and E aren't even divisible by either 2 or 5, so there's no chance any of them could ever produce a terminating decimal (technically they could if the denominator completely canceled out, and the fraction was in fact an integer, but that clearly doesn't happen here). So D is the only answer that could conceivably be right, and since the question must have a right answer, there's no need to confirm that.

EgmatQuantExpert · Answer

Solution

To find  
We need to determine
 • Among the given options, which one can be expressed as a terminating decimal

Approach and Working out  
For any given fraction, it can be expressed as a terminating decimal only when the denominator can be written in the powers of 2 and 5 only.
 • For 1/259, 259 = 7 x 37
• For 27/101, 101 = 1 x 101
• For 100/27, 27 = 3 x 3 x 3
• For 231/660 or 7/20, 20 = 2 x 2 x 5
• For 1/11, 11= 1 x 11

Thus, option D is the correct answer.

Correct Answer: Option D

bumpbot · Answer

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Which of the following fractions will terminate when express

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Which of the following fractions will terminate when express

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