How many times do you need to fold a piece of paper to make it reach the moon?

Answer 1

You need to fold an average piece of copy paper 42 times in half to reach the moon.

Here's how to figure that out:

The average distance to the moon from Earth's center is 384,403 km, and the average thickness of a sheet of paper is about .1 mm or .0000001 km.

Now, every time we fold the paper, it's thickness will double. When you repeatedly double a quantity, you can calculate what that quantity will be after a certain number of doublings with this formula:

P*2^n

where P is the original quantity, and n is the number of doublings.

Putting our number for paper thickness in:

(.0000001 km)*2^n

we find the number of folds, n, required to reach the moon by simply setting this formula equal to the distance between Earth and the moon and solving for n:

(.0000001 km)*2^n = 384,403km

2^n = 384,403 km/.0000001 km

n = log base 2 (384,403 km/.0000001 km)

n = 41.8058

Since folding only eight tenths of a time doesn't make sense, we round up to 42.