piece of construction paper is .01mm thick. It cut in half and one piece is placed on the other to make a pile. after the pieces are piled for the tenth time

Question

what will the height be in centimeters?

 

Answer 1

After the first cut, the height of the pile is 2(0.01mm).

After the second cut, the height of the pile is 2(2(0.01mm)).

After the third cut, the height of the pile is 2(2(2(0.01mm)))   [ note: the thickness of the pile doubles each time ]

. . .

After the tenth time, the height of the pile is 2(2(2(2(2(2(2(2(2(2(0.01mm)))))))))) = 2¹⁰(0.01mm)

     Note: 2¹⁰ is a very important number to remember  (1024, roughly 1K)

 

So, 1024(0.01 mm) = 10.24 mm *(1 cm / 10 mm ) = 1.024 cm

 

(practical note: I realize that this is just a math problem, but regular copy paper is often 0.1 mm thick, so this paper is really thin and not at all good for "construction paper.")