LARGE NUMBERS Estimation


GPC Enrollment :                                 1.5 x 104
# Hairs /Head :                                       3   x 105
# of Salt Grains in a Morton Bottle a:  3   x 106
Metro-Atlanta Population :                  3.5 x 106
U.S. Population b:                               2.8 x 108
World Population :                                6  x 109

# of Sand Grains in a Beach c              1 x 1015
    (100m x 10km x 1m) :
# of Chess Games Played                < 1 x 1016
                         in the past:
# of Stars in the Universe:                  1 x 1022
# of p's & n's in a Drop of Water:        5 x 1022
Avogadro's Number (= a mole) :        6 x 1023
# of Sand Grains in the worldd :         1 x 1026     ~200 moles
# of Air  Molecules in this room e:     1 x 1028
            (30ft x 40ft x 12ft)
# of p's & n's in a human body :         1 x 1028

# of  Chess Games Possible f,g :       1 x 1040 (Western)
         (under estimations)                        1 x 1060 (Korean/Chinese)
# of Water Molecules                           5 x 1046
                in Ocean Water :
# of p's & n's in Ocean Water :           1 x 1048
# of p's & n's in the Earth :                  1 x 1051
# of p's & n's in the Sun :                    1 x 1057
# of p's & n's in the Milky Way :         1 x 1068
# of p's & n's in the Universe :           1 x 1080

Googol :                                                1 x 10100
# of Go Games Possible h:                  1 x 10375  (=200!)

Googolplex:                                         1 x 10googol



Note:

a. Based on an average mass of a salt grain which is about 0.15 mg.
b. US Population  ~  4.5% of World Population
c. Assuming an average volume of a sand is 0.001cm3,
    100m x 10,000m x 1m (106cm3/m3) / 0.001cm3.
d. Assumed  that 0.01% of the volume of the Earth is sand.
    Volume of the Earth = (4/3)(3.14)(6,400 km)3 = 1.1 x 1027 cm3.
e. (30ft x 40ft x 12ft)(0.3048m/ft)3(1,000L/m3) = 410,000 L
    Divide thi volume with 24.5 L (molar volume of air at 25oC),
    then, multiply it withe Avogadro's Number, 6.022x1023.
f. Based on the average number of movement to finish a chess game:
g. Probability of repeating a same chess game
        ~  1016/1040 = 1/ 1024 (a trillionth of a trilllionth).
h. This is a  rough estimation again based on an average number of movement  to finish a Go(Badook) game.


(09/95, 09/01, revised, MHK)