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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?

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.

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

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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]

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04 Jul 2014, 04:28

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

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06 Aug 2014, 23:33

bumpbot wrote:

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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

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07 Aug 2014, 00:59

alphonsa wrote:

bumpbot wrote:

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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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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19 Sep 2016, 05:27

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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