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Is r/s^2 a terminating decimal? 1) s = 225 2) r = 81

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Is r/s^2 a terminating decimal? 1) s = 225 2) r = 81 [#permalink] New post 14 Nov 2007, 17:23
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Is r/s^2 a terminating decimal?

1) s = 225
2) r = 81
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 [#permalink] New post 14 Nov 2007, 17:30
Answer C

case 1: is S = 225. If we consider any numerator say 17, then the result will be a recurring decimal, but for numerator 9, it will be a terminating decimal. Insufficient

Case 2: similarly insufficient.

Combining together will give the equatioin 81/(225)^2 = ((9/225))^2

but 9/225 = 0.04 so its square will be 0.0016 a terminating decimal.

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 [#permalink] New post 14 Nov 2007, 17:54
OA is C.

However there are a number of rules for terminating decimals:

Denominators with prime factors other than 2 & 5 I believe are repeating.
1/17 has how many repeating numbers? (p-1) = 16 numbers

Can you confirm this?
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Re: DS - Terminating decimals [#permalink] New post 14 Nov 2007, 22:13
yuefei wrote:
Is r/s^2 a terminating decimal?

1) s = 225
2) r = 81


Answer C

A decimal is terminating only if the denominator has prime factorization of 5 and/or 2.

Stat 1: s = 225, means that the denominator includes 3 as a prime factor. Since this says nothing about the numerator we don't know if the 3's get canceled out. Insuff.

Stat 2: Says nothing about the denominator. Insuff.

Together: Tells us that the fraction is 81/225 * 225. We can answer the question. (yes) Suff.
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 [#permalink] New post 15 Nov 2007, 18:13
P is a prime number. Have you seen other applications of this rule?
  [#permalink] 15 Nov 2007, 18:13
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