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# Which of the following does NOT have a decimal equivalent that is a

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Math Expert
Joined: 02 Sep 2009
Posts: 43896
Which of the following does NOT have a decimal equivalent that is a [#permalink]

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29 Jul 2015, 14:56
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Which of the following does NOT have a decimal equivalent that is a terminating decimal?

A. 1/2^25
B. 5^3/2^7
C. 3^8/6^10
D. 3^9/6^7
E. 6^8/10^10

Kudos for a correct solution.
[Reveal] Spoiler: OA

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Which of the following does NOT have a decimal equivalent that is a [#permalink]

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29 Jul 2015, 15:04
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Bunuel wrote:
Which of the following does NOT have a decimal equivalent that is a terminating decimal?

A. 1/2^25
B. 5^3/2^7
C. 3^8/6^10
D. 3^9/6^7
E. 6^8/10^10

Kudos for a correct solution.

The rule of thumb that $$2$$s and $$5$$s in the denominator are the factors which produce terminating decimals is what I followed. A, B, and E are out, automatically, since the denomintor consist of $$2$$s and/or $$5$$s. The $$3$$s in D's denominator can be reduced to none, and thus the answer choice left is C.

IMO C.
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Re: Which of the following does NOT have a decimal equivalent that is a [#permalink]

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29 Jul 2015, 23:47
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Bunuel wrote:
Which of the following does NOT have a decimal equivalent that is a terminating decimal?

A. 1/2^25
B. 5^3/2^7
C. 3^8/6^10
D. 3^9/6^7
E. 6^8/10^10

Kudos for a correct solution.

For a fraction to have terminating decimal, it must either have only 2 and/or 5 in the denominator. All other values in the denominator leads to non terminating decimal values

Hence,
1. A has 2 in the denominator, Hence it is terminating
2. B is also terminating
3. 3^8/(6^10) can be written as 3^8/ (2^10 * 3^10) => 1/(2^10 * 3^2). There is 3 in the denominator. Hence it is non terminating decimal
4. 3^9/(2^7 * 3^7) => 3^2/2^7. Hence Terminating
5. Has both 2 & 5 in the denominator. Hence Terminating.

Option C
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Schools: ISB '18
GMAT 1: 680 Q49 V33
Re: Which of the following does NOT have a decimal equivalent that is a [#permalink]

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30 Jul 2015, 05:04
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The answer is c as after reducing the expression 3 is still left in denominator
Math Expert
Joined: 02 Sep 2009
Posts: 43896
Re: Which of the following does NOT have a decimal equivalent that is a [#permalink]

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17 Aug 2015, 06:52
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Bunuel wrote:
Which of the following does NOT have a decimal equivalent that is a terminating decimal?

A. 1/2^25
B. 5^3/2^7
C. 3^8/6^10
D. 3^9/6^7
E. 6^8/10^10

Kudos for a correct solution.

VERITAS PREP OFFICIAL SOLUTION:

The numbers in the answer choices are too involved to calculate, so here you will have to rely on pattern thinking and your knowledge of base fraction calculations. Just knowing the most common fraction-to-decimal calculations, you should know that:

1/2 = 0.5

1/3 = 0.3333333....

1/4 = 0.25

1/5 = 0.2

1/6 = 0.1666.....

So when you're dealing with prime bases of 2, 3, and 5 in denominators (as you are in this problem), when you have a base of 3 the decimals do not terminate, but when you have bases of 2 and 5 (but not combined with a base of 3) the decimals do terminate. Even for a choice like A, you should see that every time you divide 1/2 by 2, the decimals eventually do terminate: 0.5, 0.25, 0.125, 0.0625, etc. So your job here really is to determine which of these fractions leaves at least one 3 in the denominator.

Because choices A, B, and E all involve only 2s and 5s in the denominators, their decimals will eventually terminate. And because choice D has more 3s in the numerator than in the denominator, the 3s in the denominator will cancel out:

$$\frac{3^9}{(2^7)(3^7)}$$ simplifies to $$\frac{3^2}{2^7}$$, which now only has 2s in the denominator so it will terminate.

That leaves only choice C, for which only 8 of the 3s in the denominator will cancel, meaning that with two 3s left in the denominator this decimal will not terminate. C is the correct answer.
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Re: Which of the following does NOT have a decimal equivalent that is a [#permalink]

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17 Mar 2017, 05:34
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