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

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

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New post 27 Aug 2018, 11:09
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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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New post 27 Aug 2018, 14:13
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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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New post 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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