Question: Which of the following is a terminating decimal, when expressed in decimals?

1. 17/223
2. 13/231
3. 41/3
4. 41/256
5. 35/324

Answer: D

Solution and Explanation:

Approach Solution 1:

diminished fraction If and only if b (denominator) is of the form 2^n*5^m, where m and n are non-negative integers,

the fraction a / b can be represented as a terminating decimal, indicating that it has already been reduced to its lowest term. For instance, 7 / 250 is a terminating decimal of the form 0.028 since the denominator, 250, equals 2 * (5^2). Because 3 / 30=1 / 10 and the denominator is 10=2 * 5, the fraction 3 / 30 is also a terminating decimal.

RETURNING TO THE QUESTION

Since the denominator in the fraction 41/256 = 41 / (2^8) has just one prime factor, 2, this fraction will end in a digit.

All other fractions (after decreasing, if possible) will be repeated decimals because their prime factorization contains primes other than 2 and 5.

D is the correct answer.

Approach Solution 2:

If one of the following conditions is met by the denominator b, then the fraction a/b is a terminating fraction.

(1) A version of 2^n appears in the denominator.
(2) A variant of 5^m is used as the denominator.
(3) A variant of 2^n * 5^m is used as the denominator.

The fraction is not a terminating decimal if the denominator is a version of 2^n * 3^m.
Checking all the options one by one,

We can see that D is the correct answer.

“Which of the following is a terminating decimal, when" - is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been borrowed from the book “GMAT Official Guide Quantitative Review”.

To understand GMAT Problem Solving questions, applicants must possess fundamental qualitative skills. Quant tests a candidate's aptitude in reasoning and mathematics. The GMAT Quantitative test's problem-solving phase consists of a question and a list of possible responses. By using mathematics to answer the question, the candidate must select the appropriate response. The problem-solving section of the GMAT Quant topic is made up of very complicated math problems that must be solved by using the right math facts.

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