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Senior Manager
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Which of the following fractions has a decimal equivalent [#permalink]
 02 Apr 2007, 06:18
Question Stats:
0% (00:00) correct
100% (01:08) wrong based on 0 sessions
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
Any fast way of doing this?
I think no one would actually divide... 
OA: E
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Re: PS - terminating decimal [#permalink]
02 Apr 2007, 10:00
ricokevin 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 Any fast way of doing this? I think no one would actually divide... OA: ETerminating decimal --> A number having a 'fixed' number of decimal places...==> Can be expressed as N/(10^n).....
=> Deno ..i.e 10 ^n= 2^n . 5^n
i.e Deno can be expressed as factors of only 2,5 ...then it will terminate...
Here n >=0
E) has all factors in Deno as '2 ' only ....
Terminated 
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Senior Manager
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suithink,
So as far as I understood, any fraction that has a denom., which has 2 and 5 as the only prime factors, is a terminating decimal?
Is it a sufficient condition always?
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Manager
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Caas wrote: suithink,
So as far as I understood, any fraction that has a denom., which has 2 and 5 as the only prime factors, is a terminating decimal?
Is it a sufficient condition always?
The key point to be noted here is :
Terminating decimal --> A number having a 'fixed' number of decimal places...==> Can be expressed as N/ (10^n).....
=> Deno ..i.e 10 ^n= 2^n . 5^n.....
Then it means Yes...sufficient enough...
(Note the 5^n has disappaered when converting to N/10^n form a term will appear in num which will cancel out 5^n factor)
PS: BTW do a search in the forum ...this problem has been covered lot many times here...
Last edited by suithink on 02 Apr 2007, 10:41, edited 1 time in total.
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Senior Manager
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Thank you 
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Senior Manager
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http://mathforum.org/library/drmath/view/58174.html
The fraction will terminate if and only if the denominator has for
prime divisors only 2 and 5, that is, if and only if the denominator
has the form 2^a * 5^b for some exponents a >= 0 and b >= 0. The
number of decimal places until it terminates is the larger of a and b.
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Senior Manager
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Wow.
Thanks suithink and Summer3.
That's good to know. I've just jotted it down in my "math notes."
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Senior Manager
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The fraction will terminate if and only if the denominator has prime divisors only 2 and 5 or both.
A. 10/189 = 10/(3*3*3*7) Non-term.
B. 15/196 = 15/(2*2*7*7) Non-term.
C. 16/225 = 16/(5*5*3*3) Non-term.
D. 25/144 = 25/(2*2*2*7) Non-term.
E. 39/128 = 39/(2^7) Terminating because only 2 in denominator.
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VP
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upon first look, u should select E.
2 and any power of it always has terminating decimal. 5 as well.
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Manager
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Summer3 wrote: The fraction will terminate if and only if the denominator has prime divisors only 2 and 5 or both.A. 10/189 = 10/(3*3*3*7) Non-term. B. 15/196 = 15/(2*2*7*7) Non-term. C. 16/225 = 16/(5*5*3*3) Non-term. D. 25/144 = 25/(2*2*2*7) Non-term. E. 39/128 = 39/(2^7) Terminating because only 2 in denominator.
Thanks for writing STEPS so clear and easy to follow...
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Intern
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sidenote:
isn't there also a rule stating that any number divided by 4 will always terminate as well??
I remember reading it somewhere
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Director
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yes !
4 = 2^2 x 5^0
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Director
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tennis_ball wrote: upon first look, u should select E.
2 and any power of it always has terminating decimal. 5 as well.
same approach as above. 2 and its power have terminating decimal.
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Senior Manager
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just found this today. thank you to the authors.
i sort of figured this out on my own by testing... oh... i don't know about 10 or 20 numbers during a practice CAT  ) definately a huge time waster. it is nice to know the actual reasoning behind it and that it works all the time without question.
i recognized that anytime when a denominator has factors of 2 AND 5 to some power (5^0 or 2^0 still count) it is terminiating. of course any number in the denominator with other factors can lead to a terminiating decimal depending on the numerator (3/30 etc...) but i don't think that when we see a question like this they are looking to test us on that...
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Re: Which of the following fractions has a decimal equivalent [#permalink]
18 Nov 2011, 07:18
The lesson I learned today:
Be careful about nominators as well. Because sometimes test makers provide a nominator that can simplify the factors of denominator.
For example \frac{18}{225}
At first glance, 3 is a factor of denominator, so we conclude that this fraction is not terminating. but nominator is 18!
So the simplified fraction is \frac{2}{25} and terminating.
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Re: Which of the following fractions has a decimal equivalent
[#permalink]
18 Nov 2011, 07:18
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close
