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Vamshi8411
Joined: 24 Jul 2012
Last visit: 20 Oct 2013
Posts: 12
Given Kudos: 7
Schools: Schulich '16
GMAT 1: 610 Q49 V26
WE:Consulting (Consulting)
Updated on: 17 Sep 2012, 06:40
Originally posted by Vamshi8411 on 17 Sep 2012, 06:26.
Last edited by Bunuel on 17 Sep 2012, 06:40, edited 1 time in total.
Last edited by Bunuel on 17 Sep 2012, 06:40, edited 1 time in total.
Edited the question.
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
15%
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Question Stats:
76% (00:54) correct
24%
(01:20)
wrong
based on 964
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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?
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?
17 Sep 2012, 06:44
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Vamshi8411
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.
Answer: D.
For more check Number Theory chapter of Math Book: math-number-theory-88376.html
Hope it helps..
24 Jun 2013, 01:16
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prateekbhatt
Hi prateekbhatt
The fraction a/b is a terminating fraction only if the denominator b meets any of following conditions
(1) the denominator is a form of 2^n
(2) the denominator is a form of 5^m
(3) the denominator is a form of 2^n*5^m
If the denominator is a form of 2^n*3^m ==> The fraction is not terminating decimal.
Hope it helps.
