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Re: Which of the following fractions has a decimal equivalent [#permalink]

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02 Apr 2007, 10:21

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?

Re: Which of the following fractions has a decimal equivalent [#permalink]

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02 Apr 2007, 10:37

1

This post was BOOKMARKED

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.

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.

Re: Which of the following fractions has a decimal equivalent [#permalink]

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30 Jun 2007, 19:20

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...

Re: Which of the following fractions has a decimal equivalent [#permalink]

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18 Nov 2011, 07:18

1

This post received KUDOS

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]

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12 Aug 2015, 01:14

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Re: Which of the following fractions has a decimal equivalent [#permalink]

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14 Aug 2015, 04:29

[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...

The correct answer is E 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!

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