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

Question

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 .

mejia401 · Answer

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.

ashokk138 · Answer

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

longfellow · Answer

The answer is c as after reducing the expression 3 is still left in denominator

Bunuel · Answer

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 .

AndrewN · Answer

I will admit to having taken more time to solve this one--2:59--than I would like to have seen, but that is how it goes sometimes, and that just lets me know which areas I need to practice to improve my efficiency. I approached the problem in a more intuitive manner, without knowing the 2's and 5's trick, but sort of feeling out the numbers as I went along.

(A) I traced the pattern 1/4, 1/8, 1/16, and then thought that although there would be a bunch of zeros after the decimal, these even divisors would eventually lead to a terminating decimal.

(B) I actually worked the problem to 125/128, and then I thought that I might want to check other answers for more obvious tip-offs (like 1/3 or 1/9).

(C) Here, I started to work down the fractions by common factors, so this answer became  \frac{3^8}{(2^1^0 * 3^1^0)} , which ended up as
 \frac{1}{(2^1^0 * 3^2)} . That 3^2 (or 9) in the denominator looked promising...

(D) Performing the same factoring as in (C), this choice became  \frac{3^9}{(3^7 * 2^7)} , which reduced to  \frac{3^2}{2^7} , and 9 divided by an even number did not feel as promising as (C).

(E) I did not even carry out anything, since 10^10 would lead to division by 1 with a bunch of zeros.

Between (C) or (D), to be honest, the 9 of the denominator in (C) persuaded me to go for it. That is, I remembered that 1/9 is .111111, 2/9 is .222222, and so on, so I reasoned that 1 divided by 9, even if that 9 were multiplied by something else, would still lead to some sort of nonterminating decimal. Ugly, yes, but still correct.

ScottTargetTestPrep · Answer

After reducing a fraction to lowest terms, the fraction becomes a terminating decimal only if there are only factors of 5 and/or 2 in the denominator.

Since 3^8/6^10 = 3^8/(3^10 x 2^10) = 1/(3^2 x 2^10), and since a fraction (in lowest terms) that has primes other than 5 and 2 in the prime factorization of the denominator does not terminate, 3^8/6^10 does not terminate.

Answer: C

rishab0507 · Answer

terminating decimal is a decimal which has only 2's and 5's in denominator

only option C,D looks to be tested as other have 2's ,5's or are factor of both
3^9/ 6^7 , will cancel out with numerator 3^7, so left in denominator is only 2^7. thus, it is terminating decimal.

C is the answer as it will leave 3^2 in denominator even after cancelling out the numerator

bumpbot · Answer

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

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