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Decimal equivalent - GMAT prep Exam pack 1

Expert replies
Source: — Problem Solving |

by OptimusPrep » Mon May 23, 2016 10:52 am
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
I. 1/12 = 1/3*1/4
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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by Brent@GMATPrepNow » Mon May 23, 2016 12:46 pm
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
Let's say that x = a/b where the fraction a/b is written in simplest terms.

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
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by Jimit09 » Fri Jan 13, 2017 11:12 am
Brent@GMATPrepNow wrote:
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
Let's say that x = a/b where the fraction a/b is written in simplest terms.

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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by DavidG@VeritasPrep » Fri Jan 13, 2017 1:50 pm
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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by Scott@TargetTestPrep » Thu Jan 19, 2017 4:47 pm
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
This problem is testing us on our knowledge of terminating decimals.

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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