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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, 05:26
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Question Stats:

52% (01:53) correct 48% (00:46) wrong based on 75 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, 05:40, edited 1 time in total.
Edited the question.
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Re: Which of the following is a terminating decimal, when [#permalink]  17 Sep 2012, 05:44
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Expert's post
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]  23 Jun 2013, 23:48
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Re: Which of the following is a terminating decimal, when [#permalink]  24 Jun 2013, 00:12
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prateekbhatt wrote:
Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??

How can you break 2^m * 5^n into 2^m * 3^n?
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Re: Which of the following is a terminating decimal, when [#permalink]  24 Jun 2013, 00:16
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prateekbhatt wrote:
Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??

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.
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Re: Which of the following is a terminating decimal, when [#permalink]  24 Jun 2013, 00:22
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pqhai wrote:
prateekbhatt wrote:
Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??

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.

Hope it helps.

That's correct if a/b is already reduced to its lowest term.

The denominator of 3/30 is not a form of 2^n*5^m but 3/30 IS a terminating decimal, because 3 can be reduced.

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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
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Re: Which of the following is a terminating decimal, when   [#permalink] 24 Jun 2013, 00:22
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