Folding a sheet of paper to the Moon

Question

A sheet of paper is 0.1 mm thick. Each fold doubles the thickness of the stack. The Moon is about 384,000 km away. How many folds would it take for the folded stack to reach the Moon? (Pretend the paper can be folded as many times as you like.) Then estimate how many folds reach the height of a person, and how many reach the Sun.

Accepted Answer

About 42 folds. The arithmetic. After n folds the stack is 0.1 mm × 2 to the n. The Moon is 384,000 km = 3.84 × 10 to the 11 mm. We need 2 to the n to be about 3.84 × 10 to the 12. Since 2 to the 40 is about 1.1 × 10 to the 12 and 2 to the 42 is about 4.4 × 10 to the 12, 42 folds get you past the Moon (41 fall just short, at about 220,000 km). Milestones. Ten folds: 0.1 mm × 1,024, about 10 cm, a thick book. Fourteen folds: 1.6 m, a person. Twenty folds: about 100 m. Thirty folds: about 100 km, the edge of space. Forty-two folds: the Moon. Fifty-one folds: about 225 million km, past the Sun (…

Folding a sheet of paper to the Moon

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