A piece of paper is cut in half

HOME

Math Central

Quandaries & Queries

Question from Jana, a student:

A piece of paper is cut in half and one piece is placed on top of the other. Then the two pieces are cut in half and one half is placed on top of the other, forming a stack of four pieces. If this process is carried out a total of 25 times and the original piece of paper is .003 inches thick, what is the height of the stack to the nearest foot.

b. Using the same problem setup: Suppose now that our paper is big enough to fold 50 times. Again the question is "What is the height of the stack of paper," but this time, "to the nearest mile."

Hi Jana.

Each time you do the process, you double the size of the stack.

The original stack is 0.003 inches.
After 1 cut, the stack is 2 x 0.003 inches.
After 2 cuts, the stack is 2 x 2 x 0.003 inches.
After n cuts, the stack is 2ⁿ x 0.003 inches.

So after 25 cuts, the stack is 2²⁵ x 0.003 inches. Work that out and convert to feet.

For part b, do the same thing, but it is 2⁵⁰ x 0.003 inches. Convert to miles afterward.

Hope this helps,
Stephen La Rocque.

Math Central is supported by the University of Regina and The Pacific Institute for the Mathematical Sciences.