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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?

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.

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.

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]
18 Nov 2011, 06:18

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.

gmatclubot

Re: Which of the following fractions has a decimal equivalent
[#permalink]
18 Nov 2011, 06:18