Which of the following fractions has a decimal equivalent : PS Archive
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# Which of the following fractions has a decimal equivalent

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Which of the following fractions has a decimal equivalent [#permalink]

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21 Jul 2006, 19:56
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Which of the following fractions has a decimal equivalent that is a terminating decimal?

A. 10/189
B. 15/196
C. 16/225
D. 25/144
E. 39/128

Ans is E.. it is obvious but I am wondering there is a faster way to solve this one.

My reasoning is
A. 10/189 = 10/(9*21) = (10/21)(1/9)
since demonominator is multiple of 9, (1/9) is repeating decimal
no matter what the value of green, we know blue is repeating decimal. Thus x*repeating decimal = repeating decimal
B. 15/196 = no clue. Is there a short cut??
C. 16/225 = 16/(25*9) = (16/25)*(1/9) => repeating decimal
D. 25/144 = 25/(16*9) = (25/16)*(1/9) => repeating decimal
E. 39/128 = 39/2^7 = obviously terminating decimal.. divided by 2 7times.
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21 Jul 2006, 20:04
Factoring the denominator is the best soultion in my opnion. A number will not be terminating if a prime number greater than 2 is in the denominator.

A. 189 = 9 * 21
B. 196 = 2*7*2*7
C. 16/225 = 3*5*3*5
D. 25/144 = 3*4*3*4
E. 39/128 = 4*4*4*2 : Bingo.. this is the answer.
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21 Jul 2006, 20:25
ps_dahiya wrote:
Factoring the denominator is the best soultion in my opnion. A number will not be terminating if a prime number greater than 2 is in the denominator.

A. 189 = 9 * 21
B. 196 = 2*7*2*7
C. 16/225 = 3*5*3*5
D. 25/144 = 3*4*3*4
E. 39/128 = 4*4*4*2 : Bingo.. this is the answer.

I didnt know that..

This one took me less than 10 seconds
I was just wondering about the rules.

Thanks.
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21 Jul 2006, 20:32
5 .. thanks again.
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21 Jul 2006, 20:32
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# Which of the following fractions has a decimal equivalent

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