2^100

(Two to the 100th Power)

Click here to read the question


A Way to Visualize the Powers of Two

Just a simple table, but it clearly shows the progression of geometrically-increasing numbers.


  Cuts                                     Pieces   Thickness (most values rounded)

    0                                           1     0.1 mm
    1                                           2     0.2 mm
    2                                           4     0.4 mm
    3                                           8     0.8 mm
    4                                          16     1.6 mm
    5                                          32     3.2 mm
    6                                          64     6.4 mm
    7                                         128    1.28 cm
    8                                         256    2.56 cm      1 inch
    9                                         512    5.12 cm      2 inches
   10                                       1,024      10 cm      4 inches
   11                                       2,048      20 cm      8 inches
   12                                       4,096      41 cm     16 inches
   13                                       8,192      82 cm     32 inches
   14                                      16,384     1.6 m      64 inches
   15                                      32,768     3.3 m      10 feet
   16                                      65,536     6.6 m      20 feet
   17                                     131,072      13 m      40 feet
   18                                     262,144      26 m      80 feet
   19                                     524,288      52 m     160 feet
   20                                   1,048,576     105 m     320 feet
   21                                   2,097,152     210 m       1 city block
   22                                   4,194,304     420 m       2 city blocks
   23                                   8,388,608     840 m       4 city blocks
   24                                  16,777,216     1.7 km      1 mile
   25                                  33,554,432     3.4 km      2 miles
   26                                  67,108,864     6.7 km      4 miles
   27                                 134,217,728      13 km      8 miles
   28                                 268,435,456      27 km     16 miles
   29                                 536,870,912      54 km     32 miles
   30                               1,073,741,824     107 km     64 miles
   31                               2,147,483,648     215 km    128 miles
   32                               4,294,967,296     430 km    256 miles
   33                               8,589,934,592     860 km    512 miles 
   34                              17,179,869,184
   35                              34,359,738,368     Almost across the USA
   36                              68,719,476,736
   37                             137,438,953,472
   38                             274,877,906,944
   39                             549,755,813,888
   40                           1,099,511,627,776
   41                           2,199,023,255,552
   42                           4,398,046,511,104     Past the Moon
   43                           8,796,093,022,208
   44                          17,592,186,044,416
   45                          35,184,372,088,832
   46                          70,368,744,177,664
   47                         140,737,488,355,328
   48                         281,474,976,710,656
   49                         562,949,953,421,312
   50                       1,125,899,906,842,624
   51                       2,251,799,813,685,248     Past the Sun
   52                       4,503,599,627,370,496
   53                       9,007,199,254,740,992
   54                      18,014,398,509,481,984
   55                      36,028,797,018,963,968
   56                      72,057,594,037,927,936     Beyond Pluto
   57                     144,115,188,075,855,872
   58                     288,230,376,151,711,744
   59                     576,460,752,303,423,488
   60                   1,152,921,504,606,846,976
   61                   2,305,843,009,213,693,952
   62                   4,611,686,018,427,387,904
   63                   9,223,372,036,854,775,808
   64                  18,446,744,073,709,551,616
   65                  36,893,488,147,419,103,232
   66                  73,786,976,294,838,206,464
   67                 147,573,952,589,676,412,928     More than 1 light-year
   68                 295,147,905,179,352,825,856
   69                 590,295,810,358,705,651,712     Beyond Proxima Centauri
   70               1,180,591,620,717,411,303,424
   71               2,361,183,241,434,822,606,848
   72               4,722,366,482,869,645,213,696
   73               9,444,732,965,739,290,427,392
   74              18,889,465,931,478,580,854,784
   75              37,778,931,862,957,161,709,568
   76              75,557,863,725,914,323,419,136
   77             151,115,727,451,828,646,838,272     To the bright star Deneb
   78             302,231,454,903,657,293,676,544
   79             604,462,909,807,314,587,353,088
   80           1,208,925,819,614,629,174,706,176
   81           2,417,851,639,229,258,349,412,352
   82           4,835,703,278,458,516,698,824,704
   83           9,671,406,556,917,033,397,649,408
   84          19,342,813,113,834,066,795,298,816     Across the Milky Way
   85          38,685,626,227,668,133,590,597,632
   86          77,371,252,455,336,267,181,195,264
   87         154,742,504,910,672,534,362,390,528
   88         309,485,009,821,345,068,724,781,056     To the Andromeda galaxy
   89         618,970,019,642,690,137,449,562,112
   90       1,237,940,039,285,380,274,899,124,224
   91       2,475,880,078,570,760,549,798,248,448
   92       4,951,760,157,141,521,099,596,496,896
   93       9,903,520,314,283,042,199,192,993,792
   94      19,807,040,628,566,084,398,385,987,584
   95      39,614,081,257,132,168,796,771,975,168
   96      79,228,162,514,264,337,593,543,950,336
   97     158,456,325,028,528,675,187,087,900,672
   98     316,912,650,057,057,350,374,175,801,344
   99     633,825,300,114,114,700,748,351,602,688
  100   1,267,650,600,228,229,401,496,703,205,376     Past the farthest galaxy


The making of layered steel depends on this same mathematical progression.  A large number of very thin layers of two kinds of metal can be sandwiched together in a few minutes.  A block of hard steel, which can hold a very sharp edge, and a block of iron or soft steel, which resists cracking, are heated and hammered together, to give two layers.  They are hammered thin enough to fold the resulting sheet over, giving three layers.  (The two inside layers are the same metal, so fuse into one.)  If the sheet is folded ten times, 1,025 layers will result.

French pastries are made similarly.  The dough is rolled into a square, buttered, and folded in thirds so as to make three layers.  These steps are repeated, usually a total of six times, giving 729 layers.  A seventh rolling and folding will give 2,187 layers.  In French, the pastry is called mille feuille, or "thousand layers".


In order to have the stack of paper end up with pieces one centimeter square (the size of a fingernail), the original sheet would have to be the size of Pluto's orbit.  Its mass would be about the same as Earth's mass.


Sizes of city blocks vary, but a common length in the USA is 660 feet in the long direction, including the street width.  That is 8 blocks per mile.  Such blocks are typically 440 feet in the short direction, or 12 per mile.

The speed of light in vacuum is very nearly 300,000,000 meters per second.

A light-year is 9,460,536,000,000,000 meters, or about 6 trillion miles.

Observations by the Wilkinson Microwave Anisotropy Probe, reported in February 2003, indicate that the Universe is 13.7 billion years old, plus or minus 1%, and that the cosmic background radiation was emitted about 380,000 years after the Big Bang.  They also indicate that the first stars began to shine just 200 million years after the Big Bang.


The image representing the Milky Way is actually a Hubble Space Telescope image of galaxy NGC 4414.

Most of the Space images in this essay can be found in NASA's Astronomy Picture of the Day archive.

The image of the Andromeda Galaxy is copyrighted by Jason Ware, who took the photo through his 6-inch refractor telescope.   Jason Ware's website


I'd like to thank Charles and Ray Eames, Isaac Asimov, Rich Brown, and Ben Huset, without whose insight and support the existence of these pages would have been highly improbable.


HomeTo my Space and Science home page

Jeff Root
August 31, 2003