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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]

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New post Updated on: 17 Sep 2012, 06:40
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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?

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.
Edited the question.
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Re: Which of the following is a terminating decimal, when  [#permalink]

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New post 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.

Answer: D.

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]

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New post 24 Jun 2013, 01:16
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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]

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New post 24 Jun 2013, 00:48
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Is it only limited to 2^m * 5^n or we can try try to break it in 2^m * 3^n as well??
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Re: Which of the following is a terminating decimal, when  [#permalink]

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Re: Which of the following is a terminating decimal, when  [#permalink]

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New post 24 Jun 2013, 01:22
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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.

Questions to pracitice:
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
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Re: Which of the following is a terminating decimal, when  [#permalink]

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New post 07 Aug 2014, 00:33
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Re: Which of the following is a terminating decimal, when  [#permalink]

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New post 07 Aug 2014, 01:59
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Is this a 600+ question? :?

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This should be a 600+ question; however by perfect method used (as stated by Bunuel) it can be solved in hardly 5 seconds :)
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Re: Which of the following is a terminating decimal, when  [#permalink]

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New post 09 Sep 2014, 11:14
Yea,infact i actually solved in 5 seconds..! i just wish i c such type of problem in actual test :wink:
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Re: Which of the following is a terminating decimal, when  [#permalink]

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Re: Which of the following is a terminating decimal, when &nbs [#permalink] 26 Jan 2018, 20:46
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