If you were to fold a piece of paper in half 42 times, it would reach the moon.
You can count the distance with that.
It is pretty much impossible to fold a single sheet of paper more than about 8 times -- though Myth Busters once folded a giant sheet the size of a football field 10 times. The resulting thickness (after hitting it with a bulldozer) was almost a foot tall, though there was quite a bit of air mixed in with the 1,024 sheets. The formula for finding out how many of something you'll have after doubling it N number of times is as follows where O is the original number (or size in our case).
o * 2^(n)
A standard sheet of paper is about 0.1 mm so 42 folds would give us this:
0.1 * 2^(42) = 439,804,651,110 mm
That's 440 billion millimeters, or 439,804 kilometers. The moon on average is 384,400 kilometers from Earth according to Google. I'd say this checks out.
To help visualize the data, here is a quick graph that tracks the thickness of the paper for each fold.
Distance of the Moon