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# Which of the following can be expressed as a terminating decimal?

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Joined: 02 Sep 2009
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Which of the following can be expressed as a terminating decimal?  [#permalink]

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02 May 2016, 21:31
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Difficulty:

15% (low)

Question Stats:

76% (01:00) correct 24% (01:15) wrong based on 176 sessions

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Which of the following can be expressed as a terminating decimal?

A. 1/25 + 1/35
B. 1/225 + 1/1,250
C. 1/11,000 + 1/13,000
D. 1/75 + 1/35
E. 1/125 + 1/8

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Which of the following can be expressed as a terminating decimal?  [#permalink]

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23 May 2017, 19:19
Bunuel wrote:
Which of the following can be expressed as a terminating decimal?

A. 1/25 + 1/35
B. 1/225 + 1/1,250
C. 1/11,000 + 1/13,000
D. 1/75 + 1/35
E. 1/125 + 1/8

CONCEPT: A fraction will Always be terminating if the denominator of fraction in least form has no Prime factor other than 2 and 5

A. 1/25 + 1/35 --- 1/35 has prime factor 7 in denominator
B. 1/225 + 1/1,250 --- 1/225 has prime factor 3 in denominator
C. 1/11,000 + 1/13,000 --- 1/11000 has prime factor 11 in denominator
D. 1/75 + 1/35 --- 1/75 has prime factor 3 in denominator
E. 1/125 + 1/8 EVERYTHING PERFECT
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Joined: 06 Nov 2014
Posts: 1882
Re: Which of the following can be expressed as a terminating decimal?  [#permalink]

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02 May 2016, 22:54
Bunuel wrote:
Which of the following can be expressed as a terminating decimal?

A. 1/25 + 1/35
B. 1/225 + 1/1,250
C. 1/11,000 + 1/13,000
D. 1/75 + 1/35
E. 1/125 + 1/8

In such questions, it is always easier to find an answer instead of eliminating choices. Let us start with the simplest ones first.

A. 1/25 + 1/35 = 12/175 = 12/25*1/7
1/7 does is not a terminating decimal.

E. 1/125 + 1/8 = 8 + 125/ 1000 = 133/1000
This is a terminating decimal and our answer.

Correct Option: E
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Re: Which of the following can be expressed as a terminating decimal?  [#permalink]

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19 Sep 2016, 09:45
Is it possible to employ the method in which terminating decimal can be determined by expressing the numbers in the form of 2^n.5^m.? If it is correct, then only option E fits the bill. 1/5^3 + 1/2^3.
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Re: Which of the following can be expressed as a terminating decimal?  [#permalink]

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23 May 2017, 18:32
Can the trail of 2s and 5s be considered as a factor that will lead to zero? Option E, we have 125=5^3 and 8=2^3.
Bunuel,
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Posts: 2830
Re: Which of the following can be expressed as a terminating decimal?  [#permalink]

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26 May 2017, 10:47
1
2
Bunuel wrote:
Which of the following can be expressed as a terminating decimal?

A. 1/25 + 1/35
B. 1/225 + 1/1,250
C. 1/11,000 + 1/13,000
D. 1/75 + 1/35
E. 1/125 + 1/8

When solving this problem, we should remember that there is a special property about fractions that allows their decimal equivalents to terminate. This property states:

In its most-reduced form, any fraction with a denominator whose prime factorization contains only 2s, only 5s, or both 2s and 5s produces decimals that terminate. A denominator with any other prime factors produces decimals that do not terminate.

Furthermore, the sum of two terminating decimals is also a terminating decimal. Scanning out answer choices, we see that the fractions in answer choice E are 1/125 (which is 1/5^3) and 1/8 (which is 1/2^3). Since each fraction is a terminating decimal, their sum will be also a terminating decimal.

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Re: Which of the following can be expressed as a terminating decimal?  [#permalink]

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15 Jul 2018, 04:45
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Re: Which of the following can be expressed as a terminating decimal? &nbs [#permalink] 15 Jul 2018, 04:45
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