Which of the following has a decimal equivalent that is a terminating decimal?
I. 1/12
II. 1/(10^2)
III. 1/(2^10)
I only
II only
I and II
I and III
II and III
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Decimal equivalent - GMAT prep Exam pack 1
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OptimusPrep
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I. 1/12 = 1/3*1/4prata wrote:Which of the following has a decimal equivalent that is a terminating decimal?
I. 1/12
II. 1/(10^2)
III. 1/(2^10)
I only
II only
I and II
I and III
II and III
Since 1/3 is nor a terminating decimal, 1/12 will also be non terminating
II. 1/(10^2) = 0.01
III. 1/(2^10). 1 divided by any power of 2 will always be a terminating decimal
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Brent@GMATPrepNow
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Let's say that x = a/b where the fraction a/b is written in simplest terms.prata wrote:Which of the following has a decimal equivalent that is a terminating decimal?
I. 1/12
II. 1/(10^2)
III. 1/(2^10)
I only
II only
I and II
I and III
II and III
There's a nice rule that says something like,
If a/b results in a terminating decimal, then the denominator, b, MUST be the product of 2's and 5's only!
So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.
Now onto the question............
I. 1/12
Here the denominator (12) CANNOT be written as a product of 2's and 5's only. So, 1/12 will NOT result in a terminating decimal.
II. 1/(10²)
Here the denominator (10²) CAN be written as a product of 2's and 5's only. So, 1/(10²) WILL result in a terminating decimal.
III. 1/(2^10)
Here the denominator (2^10) CAN be written as a product of 2's s only. So, 1/(2^10) WILL result in a terminating decimal.
Answer: E
Cheers,
Brent
Brent Hanneson - Creator of GMATPrepNow.com
Brent@GMATPrepNow wrote:Let's say that x = a/b where the fraction a/b is written in simplest terms.prata wrote:Which of the following has a decimal equivalent that is a terminating decimal?
I. 1/12
II. 1/(10^2)
III. 1/(2^10)
I only
II only
I and II
I and III
II and III
There's a nice rule that says something like,
If a/b results in a terminating decimal, then the denominator, b, MUST be the product of 2's and 5's only!
So, for example, if b = 20, the fraction a/b will result in a terminating decimal. The same holds true for other values of b such as 4, 5, 25, 40, 2, 8, and so on.
Now onto the question............
I. 1/12
Here the denominator (12) CANNOT be written as a product of 2's and 5's only. So, 1/12 will NOT result in a terminating decimal.
II. 1/(10²)
Here the denominator (10²) CAN be written as a product of 2's and 5's only. So, 1/(10²) WILL result in a terminating decimal.
III. 1/(2^10)
Here the denominator (2^10) CAN be written as a product of 2's s only. So, 1/(2^10) WILL result in a terminating decimal.
Answer: E
Cheers,
Brent
Good explanation.Thank you:)
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DavidG@VeritasPrep
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And if you're hankering for a bit more practice on this concept, head on over here: https://www.beatthegmat.com/terminating- ... 08208.html
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Scott@TargetTestPrep
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This problem is testing us on our knowledge of terminating decimals.prata wrote:Which of the following has a decimal equivalent that is a terminating decimal?
I. 1/12
II. 1/(10^2)
III. 1/(2^10)
I only
II only
I and II
I and III
II and III
When solving this problem, we should remember that there is a special property of 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, 5s, or both produces decimals that terminate. A denominator with any other prime factors produces decimals that do not terminate.
Let's look at each Roman numeral statement and determine the prime factorization of each denominator.
I. 1/12 = 1/(2^2 x 3).
II. 1/(10^2) =1/(2^2 x 5^2)
III.1/(2^10).
We see that the only two Roman numeral statements whose fractions contain only 2s and/or 5s are II. and III.
Answer: E
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