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# decimal equivalent

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Manager
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decimal equivalent [#permalink]  09 Jul 2009, 10:29
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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
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Kudos [?]: 66 [1] , given: 3

Re: decimal equivalent [#permalink]  09 Jul 2009, 10:56
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For a fraction to be a terminating decimal the denominator can contain only the prime factors 2 and/or 5 i.e. the denominator should be in the form 2^a5^b

Looking at each denominator.

A. 189 has the prime factor 3 so the fraction is not a terminating decimal.
B. 196 has the prime factor 7 so the fraction is not a terminating decimal.
C. 225 has the prime factor 3 so the fraction is not a terminating decimal.
D. 144 has the prime factor 3 so the fraction is not a terminating decimal.
E. 128 has the prime factor 2 only and can be written in the form 2^75^0 which makes the fraction a terminating decimal.
Manager
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Re: decimal equivalent [#permalink]  09 Jul 2009, 10:58
Thanks a lot.
Nice explanation.
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Kudos [?]: 9 [2] , given: 8

Re: decimal equivalent [#permalink]  09 Jul 2009, 11:28
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KUDOS
One important point: you should look at numerator as well, as it can simplify denominator. For example, 18/225 is a terminating decimal: 18/225=\frac{3*3*2}{3*3*5*5}=\frac{2}{5*5}.
However, this problem doesn't try to trick you this way.
Re: decimal equivalent   [#permalink] 09 Jul 2009, 11:28
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