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Which of the following fractions has a decimal equivalent

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Which of the following fractions has a decimal equivalent [#permalink] New post 02 Apr 2007, 05:18
00:00
A
B
C
D
E

Difficulty:

  5% (low)

Question Stats:

50% (01:17) correct 50% (00:51) wrong based on 4 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] New post 02 Apr 2007, 09:00
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: 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 :-D
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 [#permalink] New post 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?
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 [#permalink] New post 02 Apr 2007, 09:37
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, 09:41, edited 1 time in total.
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 [#permalink] New post 02 Apr 2007, 09:38
Thank you :)
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 [#permalink] New post 02 Apr 2007, 16:23
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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 [#permalink] New post 02 Apr 2007, 16:39
Wow.

Thanks suithink and Summer3. :)

That's good to know. I've just jotted it down in my "math notes." :)
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 [#permalink] New post 02 Apr 2007, 17:01
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.

:-D
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 [#permalink] New post 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.
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 [#permalink] New post 11 Jun 2007, 18:03
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.

:-D


Thanks for writing STEPS so clear and easy to follow...
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 [#permalink] New post 11 Jun 2007, 18:38
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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 [#permalink] New post 12 Jun 2007, 22:32
yes !

4 = 2^2 x 5^0 :)
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 [#permalink] New post 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.
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 [#permalink] New post 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 :o) 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] New post 18 Nov 2011, 06:18
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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.
Re: Which of the following fractions has a decimal equivalent   [#permalink] 18 Nov 2011, 06:18
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