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

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Joined: 01 Sep 2010
Posts: 3419
Any decimal that has only a finite number of nonzero digits is a termi  [#permalink]

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27 Aug 2018, 11:09
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1
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Difficulty:

15% (low)

Question Stats:

84% (01:11) correct 16% (01:30) wrong based on 64 sessions

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Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 25, 0.09, and 8.072 are three terminating decimals. If p and q are positive integers and the ratio
$$\frac{p}{q}$$ is expressed as a decimal, is $$\frac{p}{q}$$ a terminating decimal?

(1) q is a prime number less than 10.

(2) q is not equal to 3 or 7.

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Re: Any decimal that has only a finite number of nonzero digits is a termi  [#permalink]

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27 Aug 2018, 14:13
1
carcass wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 25, 0.09, and 8.072 are three terminating decimals. If p and q are positive integers and the ratio
$$\frac{p}{q}$$ is expressed as a decimal, is $$\frac{p}{q}$$ a terminating decimal?

(1) q is a prime number less than 10.

(2) q is not equal to 3 or 7.

Question stem:- Is $$\frac{p}{q}$$ a terminating decimal?

St1:- q is a prime number less than 10.

Possible value of q: 2, 3 , 5, 7
Terminating decimal: $$\frac{p}{2}$$, $$\frac{p}{5}$$
Non-terminating decimal:$$\frac{p}{3}$$, $$\frac{p}{7}$$
Question stem is inconsistent.
Insufficient.

St2:- q is not equal to 3 or 7
a) When $$q=2^x*5^y$$ (where x and y are non-negative integers), then the ratio $$\frac{p}{q}$$ is a terminating decimal.
e.g., q=2,5,4,8,10 etc
b) When q=9, 11, 13 etc. , then the ratio $$\frac{p}{q}$$ is NOT a terminating decimal.

Insufficient.

Combined, q<10, q is prime(Primes are +ve), and $$q\neq{3}$$ or $$q\neq{7}$$
Possible values of q: $$2(=2^1*5^0)$$ and $$5(=2^0*5^1)$$

Since the denominator q is in the form $$2^x*5^y$$, hence the ratio $$\frac{p}{q}$$ is a terminating decimal..
Sufficient.

Ans. (C)
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Re: Any decimal that has only a finite number of nonzero digits is a termi  [#permalink]

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28 Aug 2018, 04:32
carcass wrote:
Any decimal that has only a finite number of nonzero digits is a terminating decimal. For example, 25, 0.09, and 8.072 are three terminating decimals. If p and q are positive integers and the ratio
$$\frac{p}{q}$$ is expressed as a decimal, is $$\frac{p}{q}$$ a terminating decimal?

(1) q is a prime number less than 10.

(2) q is not equal to 3 or 7.

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Re: Any decimal that has only a finite number of nonzero digits is a termi   [#permalink] 28 Aug 2018, 04:32
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