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# Any decimal that has only a finite number of nonzero digits

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SVP
Joined: 21 Jul 2006
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Any decimal that has only a finite number of nonzero digits [#permalink]  20 Aug 2009, 04:43
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1)Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 36, 0.72, and 3.005 are terminating decimals. If a, b, c, d and e are integers and p= 2^a3^b and q = 2^c3^d5^e , is p/q a terminating decimal?

1) a > c
2) b> d

Please explain your answer
thanks
Manager
Joined: 14 Aug 2009
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Re: Is p/p terminating decimal? [#permalink]  20 Aug 2009, 05:52
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p/p=1, man :D

the question is:
$$p= 2^a*3^b$$ and $$q = 2^c*3^d*5^e$$ , is p/q a terminating decimal?

$$p/q=2^(a-c)*3^(b-d)*5^(-c)$$
therefore, as long as (b-d)>0, p/q is terminating

Answer B
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Director
Joined: 01 Apr 2008
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Re: Is p/q terminating decimal? [#permalink]  20 Aug 2009, 09:08
Yup B.
Stmt 2 is sufficient to ensure that all 3's in the denominator are cancelled out and hence we will always have a terminating decimal
Re: Is p/q terminating decimal?   [#permalink] 20 Aug 2009, 09:08
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# Any decimal that has only a finite number of nonzero digits

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