Question

A single sheet of 20-pound bond paper is about a tenth of a millimeter thick. Each time you fold an ordinary sheet of paper in half, you double the thickness. What would be the thickness in kilometers if you were physically able to fold it 50 times? Note: For comparison, the distance from Earth to the Sun is about 149,600,000 kilometers. (Round your answer to the nearest kilometer.)

Answer 1

The paper would be 112589991 km thick if folded 50 times.

Step-by-step explanation:

Step 1; The sheet is $\frac{1}{10}$mm thick which equals 0.1 mm. Every time it is folded it doubles in thickness. So if folded once it becomes 0.2 mm thick, if folded thrice it becomes 0.4mm thick.

Thickness if folded once = $2^{1}$ × 0.1 mm

thickness if folded twice = $2^{2}$× 0.1 mm

Thickness if folded thrice = $2^{3}$ × 0.1 mm.

So if the paper is folded nth fold it would be $2^{n}$ × 0.1 mm thick.

Step 2; Using the above formula, if the paper is folded 50 times the thickness would be equal to $2^{50}$ × 0.1 mm = 112,589,990,684,262.4‬ mm.

1 km is equivalent to $10^{6}$mm so 112,589,990,684,262.4‬‬ mm = 112,589,990.6842624‬‬ km which is rounded off to 112589991 km.