Which of the following has a decimal equivalent that

[arthi9487]

Can someone please assist with the explanation for this GMAT Prep question?

Which of the following has a decimal equivalent that is a terminating decimal?

I. 1/12
II. 1/10^2
III. 1/2^10

The official answer is II and III and I just thought it was II. When I solved it looked like I and III both had repeating decimals.

[RonPurewal]

I'm going to presume that you know 1/2 is a terminating decimal (0.5).

If you know that, then, automatically, any power of that number will still be a terminating decimal -- because powers just come from multiplying the same number together a bunch of times.
E.g., (1/2)^2 is (0.5)(0.5) = 0.25. Two decimal places, since you started with one decimal place and did it twice.
Etc.

So (1/2)^10 is just going to be some decimal with exactly ten decimal places.
(You don't even need to figure out that much. All you need to understand is that, if you multiply terminating decimals together, you'll always still have a terminating decimal.)

[RonPurewal]

I'm curious what you mean by "When I solved...", since there's nothing that can actually be solved here.
Do you mean that you actually tried to multiply out 0.5 ten times?
If so, then that's quite an undertaking -- but, by the time you'd multiplied a couple of 0.5's together, you'd pretty quickly realize that you're not even going to get a repeating decimal out of that process.
So, what do you mean by that?

Thanks.

[arthi9487]

The answer choice is not (1/2)^10. It is 1/(2^10). Sorry for the confusion.

[RonPurewal]

The answer choice is not (1/2)^10. It is 1/(2^10). Sorry for the confusion.

There's actually no difference.

If the top of the fraction were something other than 1, then there would be a difference. (In the former expression, both the top and the bottom are raised to the 10th power. In the latter expression, only the bottom is.) But 1^whatever is still 1, so they are the same. Discussion unaffected. (: