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# Which of the following fractions has a decimal equivalent

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Senior Manager
Joined: 11 Feb 2007
Posts: 334
Which of the following fractions has a decimal equivalent  [#permalink]

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02 Apr 2007, 05:18
10
00:00

Difficulty:

55% (hard)

Question Stats:

55% (01:14) correct 45% (01:23) wrong based on 418 sessions

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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

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-fractions-has-a-decimal-equivalent-159322.html
Senior Manager
Joined: 20 Feb 2007
Posts: 253
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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02 Apr 2007, 17:01
8
4
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.

##### General Discussion
Manager
Joined: 15 Dec 2005
Posts: 60
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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02 Apr 2007, 09:00
3
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: E

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
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
Senior Manager
Joined: 04 Mar 2007
Posts: 401
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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02 Apr 2007, 09:21
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?
Manager
Joined: 15 Dec 2005
Posts: 60
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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Updated on: 02 Apr 2007, 09:41
1
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...

Originally posted by suithink on 02 Apr 2007, 09:37.
Last edited by suithink on 02 Apr 2007, 09:41, edited 1 time in total.
Senior Manager
Joined: 20 Feb 2007
Posts: 253
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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02 Apr 2007, 16:23
3
3
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.

Senior Manager
Joined: 11 Feb 2007
Posts: 334
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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02 Apr 2007, 16:39
1
Wow.

Thanks suithink and Summer3.

That's good to know. I've just jotted it down in my "math notes."
VP
Joined: 25 Jun 2006
Posts: 1073
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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02 Apr 2007, 22:41
upon first look, u should select E.

2 and any power of it always has terminating decimal. 5 as well.
Manager
Joined: 28 Aug 2006
Posts: 126
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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11 Jun 2007, 18:03
1
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...
Intern
Joined: 03 Apr 2006
Posts: 43
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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11 Jun 2007, 18:38
sidenote:

isn't there also a rule stating that any number divided by 4 will always terminate as well??

Director
Joined: 26 Feb 2006
Posts: 845
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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12 Jun 2007, 23:41
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.
Senior Manager
Joined: 14 Jun 2007
Posts: 391
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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30 Jun 2007, 18:20
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...
Manager
Joined: 25 May 2011
Posts: 115
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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18 Nov 2011, 06:18
1
1
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.
Manager
Joined: 10 Jun 2015
Posts: 118
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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14 Aug 2015, 03:29
[quote="ricokevin"]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...

128 = 2^7
All other denominators have factors other than 2 and 5
The basic rule is you multiply the numerator with multiples of 10 in order to get a terminating decimal.
Hope you got it!
Math Expert
Joined: 02 Sep 2009
Posts: 53066
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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16 Aug 2015, 16:21
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

OPEN DISCUSSION OF THIS QUESTION IS HERE: which-of-the-following-fractions-has-a-decimal-equivalent-159322.html
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Posts: 9892
Re: Which of the following fractions has a decimal equivalent  [#permalink]

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23 Oct 2017, 16:04
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Re: Which of the following fractions has a decimal equivalent   [#permalink] 23 Oct 2017, 16:04
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