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Which of the following fractions has a decimal equivalent th

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Which of the following fractions has a decimal equivalent th [#permalink] New post 22 Aug 2009, 10:09
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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
[Reveal] Spoiler: OA
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Re: PS: Number property [#permalink] New post 22 Aug 2009, 10:35
Is it E? If I remember correctly, the fraction will terminate only if the denominator has only 2s or 5s in its prime factorization.
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Re: PS: Number property [#permalink] New post 23 Aug 2009, 01:50
Is there any rules to solve it quickly without actual calculation?
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Re: PS: Number property [#permalink] New post 23 Aug 2009, 07:27
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I do not think you have to calculate a lot here. The rule is that the fraction terminates if the denominator has ONLY 2 or/and 5 in its prime factorization.

A 10/189...no common factors can be canceled out, and 189 is divisible by 3. The denominator does not have ONLY 2's and 5's since it has 3 in it as well. You can stop here, concluding the fraction does not terminate...
B 15/196 - no common factors can be canceled out. 196=2*2*7*7...there is a prime number 7...so the fraction does not terminate..
C 16/225...no common factors can be caceled out. decomposing the denominator 225=25*9=5^2*3^2. Does not terminate since it has 3 in its denominator
D 25/144 no common factors can be canceled out. 144= 2*72, and 72 is divisible by 3...so the fraction has 3 in its denominator...does not terminate.
E you do not have to check. you know it should be E since it is your last option. But if you want to be sure decompose the denominator and you will get only 2's in it
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Re: PS: Number property [#permalink] New post 23 Aug 2009, 17:07
Yes, OA is E.

I think Lena's explanation is good.
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Re: PS: Number property [#permalink] New post 23 Aug 2009, 23:05
if the denominator has 3 or 7 in it and can't be reduct, it must be un-terminating.

the answer is E.
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Re: PS: Number property [#permalink] New post 06 Sep 2010, 23:02
great explaination
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Re: PS: Number property [#permalink] New post 07 Sep 2010, 01:37
E. Great question.
Be suspicious about 3,7 (more suspicious if the numerator has a factor of 3 or 7). Do not blindly select the answer if the denominator alone has a 3 or 7.
If it is 8,4,2,6 then they are usually terminating.
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Re: PS: Number property [#permalink] New post 07 Sep 2010, 04:30
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Please, explain your answer. Thank you,
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Q15:
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


THEORY:

Reduced fraction \(\frac{a}{b}\) (meaning that fraction is already reduced to its lowest term) can be expressed as terminating decimal if and only \(b\) (denominator) is of the form \(2^n5^m\), where \(m\) and \(n\) are non-negative integers. For example: \(\frac{7}{250}\) is a terminating decimal \(0.028\), as \(250\) (denominator) equals to \(2*5^3\). Fraction \(\frac{3}{30}\) is also a terminating decimal, as \(\frac{3}{30}=\frac{1}{10}\) and denominator \(10=2*5\).

Note that if denominator already has only 2-s and/or 5-s then it doesn't matter whether the fraction is reduced or not.

For example \(\frac{x}{2^n5^m}\), (where x, n and m are integers) will always be terminating decimal.

(We need reducing in case when we have the prime in denominator other then 2 or 5 to see whether it could be reduced. For example fraction \(\frac{6}{15}\) has 3 as prime in denominator and we need to know if it can be reduced.)

Questions testing this concept:
700-question-94641.html?hilit=terminating%20decimal
is-r-s2-is-a-terminating-decimal-91360.html?hilit=terminating%20decimal
pl-explain-89566.html?hilit=terminating%20decimal
which-of-the-following-fractions-88937.html?hilit=terminating%20decimal

BACK TO THE ORIGINAL QUESTION:

As \(128=2^7\), then \(\frac{39}{128}\) will be terminating decimal.

Answer: E.

Hope it helps.
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Touch Question Qithout a Calculator [#permalink] New post 08 Sep 2010, 01:59
15). 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

I am interested in to know how to crack this without a calculator.

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Re: Touch Question Qithout a Calculator [#permalink] New post 08 Sep 2010, 02:30
Ans = E

the necessary and sufficient condition of terminating decimals is that the denominator's prime factors should only be 2 or 5 or both (form \(2^x * 5^y\))
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Re: Which of the following fractions has a decimal equivalent th [#permalink] New post 18 Jan 2015, 02:49
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Re: Which of the following fractions has a decimal equivalent th   [#permalink] 18 Jan 2015, 02:49
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