Intermath | Workshop Support

 Write-up

Title
Folding Paper

Problem Statement
If a piece of paper could be folded in half fifty times, what would be the thickness of the folded paper? A ream (500 sheets) of paper is 2 inches thick.

Problem setup

The problem can be set up on an excel worksheet that shows the thickness of paper folded 50 times.

Plans to Solve/Investigate the Problem

The problem statement provides the number of sheets of paper in a ream of paper and its thickness.  Because you cannot physically fold an 8-½ inch by 11-inch sheet of paper 50 times, the best way to visualize the problem is in a worksheet.

Investigation/Exploration of the Problem

The following is taken from the excel worksheet.  The inches column answers the question of thickness.

 # of Folds # of Sheets # of Reams Inches 0 1 0.002 0.004 1 2 0.004 0.008 2 4 0.008 0.016 3 8 0.016 0.032 4 16 0.032 0.064 5 32 0.064 0.128 6 64 0.128 0.256 7 128 0.256 0.512 8 256 0.512 1.024 9 512 1.024 2.048 10 1024 2.048 4.096 11 2048 4.096 8.192 12 4096 8.192 16.384 13 8192 16.384 32.768 14 16384 32.768 65.536 15 32768 65.536 131.072 16 65536 131.072 262.144 17 131072 262.144 524.288 18 262144 524.288 1048.576 19 524288 1048.576 2097.152 20 1048576 2097.152 4194.304 21 2097152 4194.304 8388.608 22 4194304 8388.608 16777.216 23 8388608 16777.216 33554.432 24 16777216 33554.432 67108.864 25 33554432 67108.864 134217.728 26 67108864 134217.728 268435.456 27 134217728 268435.456 536870.912 28 268435456 536870.912 1073741.824 29 536870912 1073741.824 2147483.648 30 1073741824 2147483.648 4294967.296 31 2147483648 4294967.296 8589934.592 32 4294967296 8589934.592 17179869.18 33 8589934592 17179869.18 34359738.37 34 1.718E+10 34359738.37 68719476.74 35 3.436E+10 68719476.74 137438953.5 36 6.8719E+10 137438953.5 274877906.9 37 1.3744E+11 274877906.9 549755813.9 38 2.7488E+11 549755813.9 1099511628 39 5.4976E+11 1099511628 2199023256 40 1.0995E+12 2199023256 4398046511 41 2.199E+12 4398046511 8796093022 42 4.398E+12 8796093022 17592186044 43 8.7961E+12 17592186044 35184372089 44 1.7592E+13 35184372089 70368744178 45 3.5184E+13 70368744178 1.40737E+11 46 7.0369E+13 1.40737E+11 2.81475E+11 47 1.4074E+14 2.81475E+11 5.6295E+11 48 2.8147E+14 5.6295E+11 1.1259E+12 49 5.6295E+14 1.1259E+12 2.2518E+12 50 1.1259E+15 2.2518E+12 4.5036E+12

Author & Contact
Susan Kelly
mailto:skelly@rockdale.k12.ga.us