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one tenth = 0.1 = 10-1
one thousandth = 0.001 = 10-3
one millionth = 0.000001 = 10-6, etc.
(1.2)
In order to get several times the above quantities one multiplies by or-
dinary numbers, so, for example, 8 × 106 =eight millions, 4 × 10-12 =four
trillionths, etc.
This notation is a vast improvement also on the one devised by the
Romans, and which was used up until the Renaissance. For example, our
galaxy, the Milky Way, has a diameter of about 105 light years (a light year
is the distance light travels in one year), in Roman numerals
105 = MMMMMMMMMMMMMMMMMMMM
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MMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMM
MMMMMMMMMMMMMMMMMMMM
The Andromeda galaxy is about 2 × 106 (two million) light years from our
galaxy, in Roman numerals writing this distance requires 40 lines.
Appendix: Examples of large numbers
Very small and very large numbers are not the sole property of cosmology,
there are many cases where such numbers appear. What is hard to do is
visualize the meaning of something like a million or a billion. Below I provide
several examples of large and small numbers.
In the table for temperatures the values are given in degrees Kelvin; a degree
Kelvin equals a degree Celsius, but zero degrees Kelvin corresponds to -273.16
degrees Celsius. In order to change to degrees Fahrenheit you need to do the
following operation:
Deg. Fahrenheit = 1.8 × Deg. Kelvin - 459.
Absolute zero, the temperature at which all systems reach their lowest energy level,
corresponds to zero degrees Kelvin, and -459 degrees Fahrenheit.
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Times (in seconds) Masses (in kilograms)
70 Lower limit to the allowed mass for a Sumo wrestler
8.6 × 104 Earth rotation time
1 000 Car
1.6 × 109 Time between Milky Way supernovae
10 000 Tyrannosaurus Rex
3 × 1013 Time for evolution of a species
1 × 1013 Typical comet mass
7.3 × 1015 Orbit time for sun around galaxy center
3 × 1014 Typical mountain mass
6 × 1016 Time for galaxy to cross a cluster
1.1 × 1016 Superterranean biomass of Earth (ocean organisms are included)
1.1 × 1017 Primeval slime to man time
5.3 × 1018 Total mass of Earth s atmosphere
1.5 × 1017 Age of Earth and Sun
3 × 1019 Typical asteroid mass
1.5 × 1017 Uranium-238 half-life
1.4 × 1021 Total mass of Earth s oceans
3 × 1017 Sun lifetime
7.3 × 1022 Mass of the Moon
3.8 × 1017 Rough age of the Milky Way
5.98 × 1024 Mass of the Earth
4 × 1017 Rough age of 47 Tucanae
1.9 × 1027 Mass of Jupiter
4.1 × 1017 Age of the universe
1.99 × 1030 Mass of the Sun
2.8 × 1030 Maximum mass for a white dwarf star
6.0 × 1030 Maximum mass for a neutron star
1.3 × 1044 Rough mass of the stars in the Coma galaxy cluster
Distances (in meters)
1.4 × 1049 Rough total mass in spiral galaxies
2 × 1052 Rough total mass of a critical density universe
1.8 Man
8 847 Height of Mount Everest
10 000 Neutron star radius
Temperatures (in deg. Kelvin)
10 000 Typical comet radius
12 000 Typical airliner cruising altitude
7 × 10-7 Laser cooling of cesium atoms
3.2 × 106 Length of the Great Wall of China
4
2.17 Liquid He superfluid transition temperature
6.3 × 106 Radius of the Earth
2.726 Cosmic microwave background temperature today
7.1 × 107 Radius of Jupiter
273 Water freezing temperature
3.8 × 108 Distance to the Moon
311 Human surface temperature
7.0 × 108 Radius of the Sun
373 Water boiling temperature
1.5 × 1011 Earth/Sun mean distance
506 Paper burning temperature
5 × 1011 Radius of the supergiant star Betelgeuse
740 Typical surface temperature of Venus
5.9 × 1012 Pluto/Sun mean distance 1811 Melting temperature of iron
5770 Solar effective temperature
9.46 × 1015 1 light-year
1.4 × 107 Center of the Sun
4 × 1016 Nearest non-solar star to Earth
5 × 107 Typical gas temperature in a cluster of galaxies
4.5 × 1016 Rough Crab Nebula radius
3 × 1010 Center of a supernova.
1.5 × 1018 Typical globular cluster radius
5.2 × 1018 Distance to the supergiant Betelgeuse
6.6 × 1019 Distance to the Crab Nebula
1.2 × 1020 Milky Way characteristic thickness
Monies (in 1994 US dollars)
2.4 × 1020 Distance from Sun to galactic center
3.9 × 1020 Milky Way disk radius
9 × 107 Development and construction cost of the Keck telescope
3 × 1022 Radius of the core of the Virgo cluster
1.5 × 108 Rough cost of a European Ariane rocket launch
7 × 1023 Distance to the center of the Virgo cluster
2.1 × 108 Total spending in the 1994 U.S. senate election campaigns
1.3 × 1027 Distance to the quasar PC 1247+3406
9 × 108 Total cost of the Magellan probe
1.1 × 109 Worldwide Visa and MasterCard fraud in 1993
1.8 × 109 Amount of food stamp fraud in the USA in 1993
3.8 × 109 Microsoft revenue in 1993
Velocities (in meters per second)
1 × 1010 Rough monetary losses associated with BCCI
1.3 × 1010 Lockheed revenue in 1993
1.5 × 1010 Rough United Nations yearly budget
1.0 × 10-9 Sea floor spreading rate
2.8 × 1010 Planned cost for the space station
1.6 × 10-9 Average slip rate of the San Andreas fault
2.6 × 1011 United States 1994 military spending
2 × 10-8 Grass growth rate
2.6 × 1011 United States 1994 predicted deficit
3 × 10-6 Typical glacial advance rate
1.3 Human walking speed 8 × 1011 United States 1994 entitlement spending
25 Car speed
1 × 1012 Rough total United States health care spending in 1994
100 Speed of an electric nervous pulse
1.3 × 1012 United States 1994 tax receipts
330 Sound speed in air
1.5 × 1012 United States 1994 federal government spending
600 Fighter jet speed
4.4 × 1012 United States 1994 national debt
2 380 Escape velocity from Moon s surface
6.4 × 1012 United States 1994 gross domestic product
11 000 Escape velocity from the Earth s surface
1.4 × 1013 United States 1994 unfunded liabilities for entitlement programs
29 000 Earth s motion around the Sun
2.2 × 105 Velocity of the Sun around the Milky Way
3.1 × 105 Escape velocity from the Milky Way
6.2 × 105 Escape velocity from the Sun s surface
5 × 106 Young (months old) supernova ejecta
2 × 108 Escape velocity from neutron star surface
3 × 108 Light in a vacuum [ Pobierz caÅ‚ość w formacie PDF ]