How many paper folds to reach the Moon?

Question

A sheet of paper is 0.1 mm thick. Each fold doubles the thickness. Solve in your head. How many folds until the stack reaches the Moon (\approx 384{,}000 km)? Aim: under 30 seconds.

Accepted Answer

Target in sheet-thicknesses: \frac{384{,}000 	ext{ km}}{0.1 	ext{ mm}} = \frac{3.84 	imes 10^8 	ext{ m}}{10^{-4} 	ext{ m}} \approx 3.8 	imes 10^{12}. Count doublings with 2^{10} \approx 10^3: - 2^{40} \approx (10^3)^4 	imes 1.1 \approx 1.1 	imes 10^{12}, short. - 2^{41} \approx 2.2 	imes 10^{12}, still short (that's about 220,000 km). - 2^{42} \approx 4.4 	imes 10^{12}, past the Moon (\approx 440{,}000 km). About 42 folds. Takeaway. Exponentials devour orders of magnitude: 12 orders of magnitude cost only \sim 40 doublings. The working kit is 2^{10} \approx 10^3 (so n orders of magn…

How many paper folds to reach the Moon?

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