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# Does the decimal equivalent of P/Q, where P and Q are

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Manager
Joined: 23 Mar 2008
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Does the decimal equivalent of P/Q, where P and Q are [#permalink]  07 Jun 2008, 10:47
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Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only a finite number of nonzero digits?

1) P>Q
2) Q=8
Director
Joined: 12 Apr 2008
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Schools: Oxford
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Re: DS: decimal equivalent [#permalink]  07 Jun 2008, 12:33
I think it’s B.
(1) insuff. Example: 3/2=1.5 finite. 5/3 = 1.66666… infinite.
(2) suff. First, note that 1/8 = 0.125. Then, for any P, P/8 = P*(1/8) = P*0.125 – finite.
Director
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Re: DS: decimal equivalent [#permalink]  07 Jun 2008, 12:42
puma wrote:
Does the decimal equivalent of P/Q, where P and Q are positive integers, contain only a finite number of nonzero digits?

1) P>Q
2) Q=8

If the fraction is reduced as much as possible, the quotient should contain only factors of 2 and/or 5 for it to be a finite terminating decimal

1) clearly not sufficient 3/2 = 1.5 , 4/3 = 1.333333333333 as examples

2) sufficient since Q = 2^3 therefore we are guaranteed to have a factor of two in the quotient after reducing the fraction.

B
Manager
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Re: DS: decimal equivalent [#permalink]  07 Jun 2008, 13:08
Yup B it is...multiples of 2 in the deno will give non terminating decimals..
SVP
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Re: DS: decimal equivalent [#permalink]  08 Jun 2008, 05:45
B for me as well. If a denominator has only 5s or only 2s as its prime factors, then the decimal will be non-terminating
Re: DS: decimal equivalent   [#permalink] 08 Jun 2008, 05:45
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# Does the decimal equivalent of P/Q, where P and Q are

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