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Which of the following is a terminating decimal, when
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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?
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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.
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Re: Which of the following is a terminating decimal, when
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17 Sep 2012, 06:44
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 nonnegative 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: mathnumbertheory88376.htmlHope it helps..
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Re: Which of the following is a terminating decimal, when
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24 Jun 2013, 01:16
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
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24 Jun 2013, 00:48
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
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24 Jun 2013, 01:12
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
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24 Jun 2013, 01:22
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: doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.html
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Re: Which of the following is a terminating decimal, when
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07 Aug 2014, 01:59
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Re: Which of the following is a terminating decimal, when
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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
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Re: Which of the following is a terminating decimal, when
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Re: Which of the following is a terminating decimal, when
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