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- 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