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# Which of the following fractions has a decimal equivalent

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Director
Joined: 08 Jul 2004
Posts: 596
Which of the following fractions has a decimal equivalent [#permalink]

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25 Sep 2004, 16:02
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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
Intern
Joined: 22 Mar 2004
Posts: 25
Location: TX

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25 Sep 2004, 16:19
C.

cos any number ending with a 5 when used as a divisor, will result in a terminating decimal
Director
Joined: 31 Aug 2004
Posts: 606

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25 Sep 2004, 16:47
Longhorn,

Could you please elaborate on this ?
Do you have any theoretical explaination ?
Director
Joined: 20 Jul 2004
Posts: 592

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25 Sep 2004, 17:28
Very good question.

I will choose E.
All other choices have a odd prime number in the denominator whereas E has only 2s.

Divide any number by an odd prime and it is going to be infinite. Anything with only 2s in denominator is finite; it either ends as a whole number or 0.5
Director
Joined: 08 Jul 2004
Posts: 596

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25 Sep 2004, 17:37
Yes, that is what I thought. 225 is 15 square has 3 in it. 128 is 2^7 , so always give 0.5. Others are square which has 3 and 189 has 7 to make non-terminating.
Cheers.
S
Director
Joined: 31 Aug 2004
Posts: 606

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27 Sep 2004, 02:49
Hardworker;

I agree with you : dividing any number with any odd prime will provide something unterminated.
What do you mean exactly by 2s ?
Manager
Joined: 26 Sep 2004
Posts: 136

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27 Sep 2004, 06:28
Hardworker , correct answer .. by the way longhorn guy yur theory is false
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Franky
http://franky4gmat.blogspot.com

Director
Joined: 08 Jul 2004
Posts: 596

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27 Sep 2004, 06:31
No, i think Longhorn is right but in all cases 5 is compunded with 3 to make non terminating.
S
Manager
Joined: 26 Sep 2004
Posts: 136

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27 Sep 2004, 06:51
Any number terminating in 5 shall give a terminating decimal, this theory is false , exactly for the exception yu mentioned, and 3 is not just the only combination.
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Franky
http://franky4gmat.blogspot.com

Intern
Joined: 25 Sep 2004
Posts: 21
Re: PS Any better way to this? [#permalink]

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28 Sep 2004, 01:34
saurya_s 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 number that either only contains: 2 or powers of 2 in the denominator OR 5 or powers of 5 OR mixture of powers of 2 and 5 (for example: 20 (2^2*5) ) would be eligible as a terminating decimal.

Therefore answer in this case is E

I hope that helps!
Director
Joined: 31 Aug 2004
Posts: 606

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28 Sep 2004, 11:00

I am not sure i understand your theory :

In case of your 2^n5^p denominator, what happens if numerator is a power of 3 ?? unterminated...
Intern
Joined: 25 Sep 2004
Posts: 21

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29 Sep 2004, 05:34
twixt wrote:

I am not sure i understand your theory :

In case of your 2^n5^p denominator, what happens if numerator is a power of 3 ?? unterminated...

Hi Twixt

Which of power 3 in the numerator is giving you an unterminated result, apply my conclusion to any number contaning anything in the numerator, but the denomiator should only have powers of 2 or powers of 5 or a mixture of powers 2 and 5. It holds for all nos.

Director
Joined: 20 Jul 2004
Posts: 592

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29 Sep 2004, 07:52
twixt wrote:
I am not sure i understand your theory :
In case of your 2^n5^p denominator, what happens if numerator is a power of 3 ?? unterminated...

Yes. See examples below. I will take a common prime numerator, say 43.

43/32 -> terminating decimal -> Since it has only 2 as prime factor
43/625 -> terminating decimal -> Since it has only 5 as prime factor
43/50 -> terminating decimal -> Since it has only 2 and 5 as prime factors
43/150 -> not a terminating decimal -> Since it has 3 as a prime factor apart from 2 and 5
43/41 -> not a terminating decimal -> Since it does not have 2 or 5 as a prime factor.

I will rephrase my statement above: Any fraction with a denominator containing prime factors of only 2 and 5, will be have terminating decimal.
Director
Joined: 31 Aug 2004
Posts: 606

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30 Sep 2004, 08:11
I was confused by the choices and the added prime 3.

I tried this with various numbers and it works : thank you guys for this nice trick !
30 Sep 2004, 08:11
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