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Terminating Decimal

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by vittalgmat » Wed Dec 31, 2008 9:32 pm
Hi folks,
I read somewhere that in a terminating decimal, the denominator will have ONLY either 2 and/or 5 as the prime factors.

Is the above stmt true??

If it is true, lets assume we a DS question as follows

Is r/s^2 a terminating decimal?

1. r = 19
2. s = 2^25* 5^500

B should be the answer ? right??

Pls let me know your thoughts.

thanks
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by scoobydooby » Wed Dec 31, 2008 9:47 pm
for a terminating decimal the denominator must be 2 or a multiple of 2 or 5 or mulitple of 5

the rule is correct
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by Ian Stewart » Thu Jan 01, 2009 12:19 am
The rule is correct *if* your fraction is reduced. 3/30 is a terminating decimal despite having a 3 in the denominator - it is not, however, a reduced fraction. Yes, the answer would be B to the DS question Vittal asks above.

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by vittalgmat » Thu Jan 01, 2009 2:42 am
Thanks Ian,
To summarize, to verify whether a fraction is a terminating decimal or not, do the foll.

1. If the fraction is reducible, reduce it.
2. If the denominator of the reduced fraction can be expressed in terms of powers of 2 and/or powers of 5 ONLY, then the fraction IS a Terminating fraction Else it is not.



And Happy new 2009 to everybody. May everyone's GMAT dream come true.
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by cramya » Thu Jan 01, 2009 4:09 pm
Stewart,
HAPPY NEW YEAR!

Feel free to correct me here. It can be just 2^ something or 5^ something or both in the denominator after the fraction is reduced for the fraction to produce a terminating decimal.

Its always easy to make up a 2^0 or 5^0 lets say if only the other exists.

Is 3/25 a terminating decimal-> Yes

3 / 2^0*5^2

Vittal,
Thanks for the summarization of terminating decimal concepts!
Happy new year!


Regards,
Cramya
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by Ian Stewart » Thu Jan 01, 2009 4:25 pm
Yes, exactly right - so the following are all terminating decimals:

7/125
9/80
7/16

because, prime factorizing the denominators, 125 = 5^3, 80 = 2^4 * 5, and 16 = 2^4; we only have 2's and/or 5's. The following are *not* terminating:

4/75
11/30
17/175

because in each case, the fraction is reduced, and the denominator is divisible by a prime different from 2 or 5 (in the first two cases, the denominator is divisible by 3, and in the last case by 7).

Finally, the following might, at first glance, appear to represent *non*-terminating decimals, but they are terminating - you must reduce the fraction first:

11/275
81/216
49/280

If we reduce these fractions, we can see that we should get terminating decimals in each case: 11/275 = 1/25, 81/216 = 3/8 and 49/280 = 7/40.
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by cramya » Thu Jan 01, 2009 4:31 pm
Excellent! Thank you once more, Ian!
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