Doubling Paper
Double, Double, Double!
What if we could fold paper again and again? How thick would it get?
Let us start with a piece of paper that is 0.1 mm thick, and keep folding it in half.
(Note: it is very hard to go beyond the 6th fold, just try it! But let us imagine we can.)
The table is below:
Folds
Size
Scientific Notation
Example values
0
0.1 mm
1.00 × 10-4 m
1
0.2 mm
2.00 × 10-4 m
2
0.4 mm
4.00 × 10-4 m
3
0.8 mm
8.00 × 10-4 m
a credit card is about 1mm thick
4
1.6 mm
1.60 × 10-3 m
5
3.2 mm
3.20 × 10-3 m
6
6.4 mm
6.40 × 10-3 m
7
12.8 mm
1.28 × 10-2 m
8
25.6 mm
2.56 × 10-2 m
an inch is 25.4 mm
9
51.2 mm
5.12 × 10-2 m
10
102 mm
1.02 × 10-1 m
11
205 mm
2.05 × 10-1 m
12
410 mm
4.10 × 10-1 m
13
819 mm
8.19 × 10-1 m
14
1.64 m
1.64 × 100 m
1.7 m is a typical height of a man
15
3.28 m
3.28 × 100 m
16
6.55 m
6.55 × 100 m
two storey house
17
13.1 m
1.31 × 101 m
18
26.2 m
2.62 × 101 m
19
52.4 m
5.24 × 101 m
20
105 m
1.05 × 102 m
21
210 m
2.10 × 102 m
22
419 m
4.19 × 102 m
23
839 m
8.39 × 102 m
almost 1 km
24
1.68 km
1.68 × 103 m
a mile is 1.609344 km
25
3.36 km
3.36 × 103 m
26
6.71 km
6.71 × 103 m
height of Mount Everest is 8.848 km
27
13.4 km
1.34 × 104 m
28
26.8 km
2.68 × 104 m
29
53.7 km
5.37 × 104 m
30
107 km
1.07 × 105 m
edge of space (100 km)
31
215 km
2.15 × 105 m
32
429 km
4.29 × 105 m
International Space Station orbit (410 km)
33
859 km
8.59 × 105 m
1 Mm (Megameter) is 1000 km
34
1.72 Mm
1.72 × 106 m
35
3.44 Mm
3.44 × 106 m
36
6.87 Mm
6.87 × 106 m
(Earth's radius is about 6.37 Mm)
37
13.7 Mm
1.37 × 107 m
(Earth's diameter is about 12.74 Mm)
38
27.5 Mm
2.75 × 107 m
39
55.0 Mm
5.50 × 107 m
40
110 Mm
1.10 × 108 m
41
220 Mm
2.20 × 108 m
42
440 Mm
4.40 × 108 m
beyond the Moon!
43
880 Mm
8.80 × 108 m
1 Gm (Gigameter) is 1 million kilometers
44
1.76 Gm
1.76 × 109 m
45
3.52 Gm
3.52 × 109 m
46
7.04 Gm
7.04 × 109 m
47
14.1 Gm
1.41 × 1010 m
48
28.1 Gm
2.81 × 1010 m
49
56.3 Gm
5.63 × 1010 m
50
113 Gm
1.13 × 1011 m
beyond Mars
51
225 Gm
2.25 × 1011 m
52
450 Gm
4.50 × 1011 m
53
901 Gm
9.01 × 1011 m
beyond Jupiter
1 Tm (Terameter) is 1 billion km
1 Tm (Terameter) is 1 billion km
54
1.80 Tm
1.80 × 1012 m
55
3.60 Tm
3.60 × 1012 m
56
7.21 Tm
7.21 × 1012 m
beyond Neptune
57
14.4 Tm
1.44 × 1013 m
58
28.8 Tm
2.88 × 1013 m
59
57.6 Tm
5.76 × 1013 m
60
115 Tm
1.15 × 1014 m
61
231 Tm
2.31 × 1014 m
62
461 Tm
4.61 × 1014 m
63
922 Tm
9.22 × 1014 m
1 Pm (Petameter) is 1 Trillion km
64
1.84 Pm
1.84 × 1015 m
65
3.69 Pm
3.69 × 1015 m
66
7.38 Pm
7.38 × 1015 m
1 light-year is 9.46 Pm
67
14.8 Pm
1.48 × 1016 m
68
29.5 Pm
2.95 × 1016 m
69
59.0 Pm
5.90 × 1016 m
beyond Alpha Centauri
70
118 Pm
1.18 × 1017 m
71
236 Pm
2.36 × 1017 m
72
472 Pm
4.72 × 1017 m
73
944 Pm
9.44 × 1017 m
1 Em (Exameter) is 1000 Pm
74
1.89 Em
1.89 × 1018 m
75
3.78 Em
3.78 × 1018 m
76
7.56 Em
7.56 × 1018 m
77
15.1 Em
1.51 × 1019 m
78
30.2 Em
3.02 × 1019 m
79
60.4 Em
6.04 × 1019 m
80
121 Em
1.21 × 1020 m
81
242 Em
2.42 × 1020 m
beyond our Galaxy
82
484 Em
4.84 × 1020 m
83
967 Em
9.67 × 1020 m
1 Zm (Zettameter) is 1000 Em
84
1.93 Zm
1.93 × 1021 m
85
3.87 Zm
3.87 × 1021 m
86
7.74 Zm
7.74 × 1021 m
87
15.5 Zm
1.55 × 1022 m
88
30.9 Zm
3.09 × 1022 m
89
61.9 Zm
6.19 × 1022 m
90
124 Zm
1.24 × 1023 m
91
248 Zm
2.48 × 1023 m
92
495 Zm
4.95 × 1023 m
93
990 Zm
9.90 × 1023 m
1 Ym (Yottameter) is 1000 Zm
94
1.98 Ym
1.98 × 1024 m
95
3.96 Ym
3.96 × 1024 m
96
7.92 Ym
7.92 × 1024 m
97
15.8 Ym
1.58 × 1025 m
98
31.7 Ym
3.17 × 1025 m
99
63.4 Ym
6.34 × 1025 m
100
127 Ym
1.27 × 1026 m
101
254 Ym
2.54 × 1026 m
102
507 Ym
5.07 × 1026 m
beyond the Observable Universe (radius of 440 Ym)
So (if we could physically do it) then 102 doublings of paper would extend beyond the observable universe!
In a way it is comforting that two things we understand (doubling, and the number 102) can reach so far.