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# Which of the following is a terminating decimal, when

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Which of the following is a terminating decimal, when [#permalink]  17 Sep 2012, 06:26
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41% (01:42) correct 58% (00:46) wrong based on 3 sessions
Which of the following is a terminating decimal, when expressed in decimals?

A. 17/223
B. 13/231
C. 41/3
D. 41/256
E. 35/324

Can we do this just by taking the unit digit in numerator and denominator?
[Reveal] Spoiler: OA

Last edited by Bunuel on 17 Sep 2012, 06:40, edited 1 time in total.
Edited the question.
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Kudos [?]: 9553 [1] , given: 826

Re: Which of the following is a terminating decimal, when [#permalink]  17 Sep 2012, 06:44
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Vamshi8411 wrote:
Which of the following is a terminating decimal, when expressed in decimals?

A. 17/223
B. 13/231
C. 41/3
D. 41/256
E. 35/324

Can we do this just by taking the unit digit in numerator and denominator?

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*5^2. Fraction \frac{3}{30} is also a terminating decimal, as \frac{3}{30}=\frac{1}{10} and denominator 10=2*5.

BACK TO THE QUESTION:

\frac{41}{256}=\frac{41}{2^8}, denominator has only prime factor 2 in its prime factorization, hence this fraction will be terminating decimal.

All other fractions (after reducing, if possible) have primes other than 2 and 5 in its prime factorization, hence they will be repeated decimals.

For more check Number Theory chapter of Math Book: math-number-theory-88376.html

Hope it helps..
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Re: Which of the following is a terminating decimal, when   [#permalink] 17 Sep 2012, 06:44
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