Paper folding

The trick is to use estimation

call the distance to the moon "d"

call the thickness of a piece of paper "t"

call the number of times you have to fold the paper (the answer to the problem) "n"

(2^n)t = d

t is around 0.2mm

0.2mm = 0.02cm = 0.0002m = 2 x10^-4 m

d = 384,400km which is around 400,000km

400,000km = 4 x10^5 km = 4 x10^8 m

2^n x 2 x10^-4 = 4 x10^8

2^n x10^-4 = 2 x10^8

2^(n-1) x10^-4 = 10^8

2^(n-1) = 10^12

10 is around 2^3, so 2 is around 10^(1/3)

10^((n-1)/3) = 10^12

(n-1)/3 = 12

n-1 = 36

n = 37, which is around 40

An excellent question. If the paper is folded (ie doubled) 10 times, it becomes 1000 sheets (1024 to be exact), if 20 times, it is a million sheets, if 30 times, it is a billion sheets, if 40 times, it is a trillion sheets, that is 10^12. Which is another way of saying that 2^40 = 10^12.

Google the distance to the moon and divide it by 10^12 to get the thickness of the paper which must be used, with 40 folds, which is (384000/10^12) km = 0.4 mm.
So the option 40 folds is the ONLY option which gives any reasonable thickness of paper. Choose any other option, and your paper will probably be less than one atom thick.

The next option after 40 is 400. Your calculator won't tell you this, but 2^400 = 10^120, which means 10^120 sheets of paper if folded 400 times. Thickness of each sheet = 384000 Km / 10^120 = 4x(10^5)x(10^6)/(10^120)mm = 4 x 10^{-109} mm