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Which of the following fractions has a decimal equivalent [#permalink]
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07 Sep 2013, 03:57
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Which of the following fractions has a decimal equivalent that is a terminating decimal? a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128
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Re: Which of the following fractions has a decimal equivalent [#permalink]
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salsal wrote: Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128 is there any simple method to find it?



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akankshasoneja wrote: salsal wrote: Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128 is there any simple method to find it? Denominators of options a,c,d contains powers of 3...numerators of these options when divided by 3 will have nonterminating decimals Denominator of option b contains power of 7...numerator 15 when divided by 7 will give non terminating decimal Option E has denominator in powers of 2...so when 39 divided by 2 will give a terminating decimal Hope it helps



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Re: Which of the following fractions has a decimal equivalent [#permalink]
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salsal wrote: Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128 THEORY: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 \(2*5^3\). Fraction \(\frac{3}{30}\) is also a terminating decimal, as \(\frac{3}{30}=\frac{1}{10}\) and denominator \(10=2*5\). Note that if denominator already has only 2s and/or 5s then it doesn't matter whether the fraction is reduced or not. For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be the terminating decimal. We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced. BACK TO THE QUESTION:Only option E (when reduced to its lowest form) has the denominator of the form \(2^n5^m\): 39/128=39/2^7. Answer: E. Questions testing this concept:doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope it helps.
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Re: Which of the following fractions has a decimal equivalent [#permalink]
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07 Sep 2013, 10:07
You can solve this question in less than 30 seconds if you understand the concept of terminating decimal. The denominator must have only power's of 2 or 5 in the denominator no other powers ( if it has any other prime factors like 3,7, etc it won't be terminating). 2's and 5's can be in any possible combination but it must only have 2's and 5's a) 10/189 denominator sum of digits is 18 so its divisible by 3 eliminate b) 15/196 This has a prime factor of 7 when do the prime factorization of the denominator.. Eliminate c) 16/225 denominator sum of digits is 9 so its divisible by 3 eliminate d) 25/144 denominator sum of digits is 9 so its divisible by 3 eliminate e) 39/128 Jackpot Correct answer
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Re: Which of the following fractions has a decimal equivalent [#permalink]
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07 Sep 2013, 10:18
That's true bunuel. Thanks for pointing out
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Bunuel wrote: salsal wrote: Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128 THEORY: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 \(10=2*5\). Note that if denominator already has only 2s and/or 5s then it doesn't matter whether the fraction is reduced or not. For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be the terminating decimal. We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced. BACK TO THE QUESTION:Only option E (when reduced to its lowest form) has the denominator of the form \(2^n5^m\): 39/128=39/2^7. Answer: E. Questions testing this concept:doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope it helps. Typo? you mean \(2*5^3\) ?



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Re: Which of the following fractions has a decimal equivalent [#permalink]
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01 Oct 2013, 19:02
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Bunuel wrote: salsal wrote: Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128 THEORY: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 \(10=2*5\). Note that if denominator already has only 2s and/or 5s then it doesn't matter whether the fraction is reduced or not. For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be the terminating decimal. We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced. BACK TO THE QUESTION:Only option E (when reduced to its lowest form) has the denominator of the form \(2^n5^m\): 39/128= 39/2^7. Answer: E. Questions testing this concept:doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope it helps. I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128



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Re: Which of the following fractions has a decimal equivalent [#permalink]
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02 Oct 2013, 03:18
AccipiterQ wrote: Bunuel wrote: salsal wrote: Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128 THEORY: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 \(10=2*5\). Note that if denominator already has only 2s and/or 5s then it doesn't matter whether the fraction is reduced or not. For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be the terminating decimal. We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced. BACK TO THE QUESTION:Only option E (when reduced to its lowest form) has the denominator of the form \(2^n5^m\): 39/128= 39/2^7. Answer: E. Questions testing this concept:doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope it helps. I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128 Yes, it is 128 = 2^7*5^0.
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Re: Which of the following fractions has a decimal equivalent [#permalink]
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02 Oct 2013, 03:19
Skag55 wrote: Bunuel wrote: salsal wrote: Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128 THEORY: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 \(10=2*5\). Note that if denominator already has only 2s and/or 5s then it doesn't matter whether the fraction is reduced or not. For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be the terminating decimal. We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced. BACK TO THE QUESTION:Only option E (when reduced to its lowest form) has the denominator of the form \(2^n5^m\): 39/128=39/2^7. Answer: E. Questions testing this concept:doesthedecimalequivalentofpqwherepandqare89566.htmlanydecimalthathasonlyafinitenumberofnonzerodigits101964.htmlifabcdandeareintegersandp2a3bandq2c3d5eispqaterminatingdecimal125789.html700question94641.htmlisrs2isaterminatingdecimal91360.htmlplexplain89566.htmlwhichofthefollowingfractions88937.htmlHope it helps. Typo? you mean \(2*5^3\) ? Yes. Edited. Thank you. +1.
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Re: Which of the following fractions has a decimal equivalent [#permalink]
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02 Oct 2013, 07:12
Bunuel wrote: AccipiterQ wrote:
I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128
Yes, it is 128 = 2^7*5^0. So ANY number with a 2^x or 5^x (where x is greater than or equal to 1) will fall into this then? I'm confused though, so 6/15 a terminating decimal, because 15 is 5^1*3^1*2^0, but then why is 16/225 is not terminating? It follows the same pattern; 225 is 5^2*3^2*2^0



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Re: Which of the following fractions has a decimal equivalent [#permalink]
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02 Oct 2013, 08:35
AccipiterQ wrote: Bunuel wrote: AccipiterQ wrote:
I'm confused, 128 is 2^7, you said it had to be 2^n*5^m....there is no 5^m in 128
Yes, it is 128 = 2^7*5^0. So ANY number with a 2^x or 5^x (where x is greater than or equal to 1) will fall into this then? I'm confused though, so 6/15 a terminating decimal, because 15 is 5^1*3^1*2^0, but then why is 16/225 is not terminating? It follows the same pattern; 225 is 5^2*3^2*2^0 Please read again: whichofthefollowingfractionshasadecimalequivalent159322.html#p12646736/15=6/(3*5) is a terminating decimal because extra 3 in the denominator is reduced and we get 2/5 (the denominator is in the form of 2^n*5^m). 16/225=16/(3^2*5^2) is not a terminating decimal because extra 3^2 in the denominator is not reduced to get the denominator in the form of 2^n*5^m. Hope it's clear.
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Re: Which of the following fractions has a decimal equivalent [#permalink]
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02 Oct 2013, 09:36
I'm a dummy! I forgot my 4th grade teachers directive to always make sure fractions are reduced haha
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Re: Which of the following fractions has a decimal equivalent [#permalink]
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12 Feb 2016, 14:21
So the numerator in this situation is irrelevant?



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Re: Which of the following fractions has a decimal equivalent [#permalink]
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13 Feb 2016, 05:16
every terminating decimal has 10,100,1000,10000 etc. in denominator when written as fraction. So, all fractions should have only 2 and/or 5 as a factors in their reduced state
a) 10/189, it is reduced, and 189 does not have any 2 or 5 b) 15/196, reduced, and 196=(2*7)^2, so does not fit c) 16/225, reduced, and 225=(3*5)^2, so does not fit d) 25/144, reduced, and 144=(3*4)^2, so does not fit e) 39/128, reduced, and 128=2^7, so can have 10^7 in denominator and fits
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Re: Which of the following fractions has a decimal equivalent [#permalink]
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salsal wrote: Which of the following fractions has a decimal equivalent that is a terminating decimal?
a) 10/189 b) 15/196 c) 16/225 d) 25/144 e) 39/128 NOTE: this is one of those questions that require us to check/test each answer choice. In these situations, always check the answer choices from E to A, because the correct answer is typically closer to the bottom than to the top. For more on this strategy, see my article: http://www.gmatprepnow.com/articles/han ... questions Cheers, Brent
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