Powers of Ten
In dealing with VERY LARGE
NUMBERS (Astronomy, High Energy Particle Accelerators) or VERY
SMALL NUMBERS (cells, molecules, atoms, nuclei, quarks) it is most convenient to
use "Powers of Ten" notation.
VERY LARGE NUMBERS:
"in words" |
"in words" |
||
| One | 100 | 1. | "ten to the zero" |
| ten | 101 | 10. | "ten to the one" |
| hundred | 102 | 100. | "ten to the two" |
| thousand | 103 | 1,000. | "ten to the three" |
| ten thousand | 104 | 10,000. | "ten to the four" |
| hundred thousand | 105 | 100,000. | "ten to the five" |
| million | 106 | 1,000,000. | "ten to the six" |
| ten million | 107 | 10,000,000. | "ten to the seven" |
| hundred million | 108 | 100,000,000. | "ten to the eight" |
| billion | 109 | 1,000,000,000. | "ten to the nine" |
| ten billion | 1010 | 10,000,000,000. | "ten to the ten" |
| hundred billion | 1011 | 100,000,000,000. | "ten to the eleven" |
| trillion | 1012 | 1,000,000,000,000. | "ten to the twelve" |
| ten trillion | 1013 | 10,000,000,000,000. | "ten to the thirteen" |
| hundred trillion | 1014 | 100,000,000,000,000. | "ten to the fourteen" |
The
names "billion" and "trillion" mean different things in different
countries. This is the US version.
There are a few more names after "trillion", but they are almost never used.
VERY SMALL NUMBERS:
"in words" |
"in words" |
||
| One | 100 | 1. | "ten to the zero" |
| tenth | 10-1 | 0.1 | "ten to the minus one" |
| hundredth | 10-2 | 0.01. | "ten to the minus two" |
| thousandth | 10-3 | 0.001. | "ten to the minus three" |
| ten thousand | 10-4 | 0.0001. | "ten to the minus four" |
| hundred thousandth | 10-5 | 0.00001. | "ten to the minus five" |
| millionth | 10-6 | 0.000001 | "ten to the minus six" |
| ten millionth | 10-7 | 0.0000001. | "ten to the minus seven" |
| hundred millionth | 10-8 | 0.00000001. | "ten to the minus eight" |
| billionth | 10-9 | 0.000000001. | "ten to the minus nine" |
| ten billionth | 10-10 | 0.0000000001. | "ten to the minus ten" |
| hundred billionth | 10-11 | 0.00000000001. | "ten to the minus eleven" |
| trillionth | 10-12 | 0.000000000001 | "ten to the minus twelve" |
| ten trillionth | 10-13 | 0.0000000000001. | "ten to the minus thirteen" |
| hundred trillionth | 10-14 | 0.00000000000001. | "ten to the minus fourteen" |
EXAMPLES of LARGE NUMBERS:
1 AU = 150,000,000 km = 1.5x l08 km = 9.2 x l07miles
Mass of the Sun = 1 Solar Mass = 2.0 x 1030 kg
1 kilometer = 1 km = 103 m ~ 5/8 mile
Energies of Fermilab's Chain of Accelerators:
Cockroft Walton: 750 KeV (Kilo-electron volts, thousand
electron volts)
= 750 times 103 electron volts
Linac (Linear Accelerator): 400 MeV ( Mega electron volts, million electron volts)
= 400 times 106 electron volts
Booster, Recycler, Debuncher, Accumulator accelerators:
8 GeV (Giga-electron volts, billion
(U.S.) electron volts)
= 8 times 109
electron volts
Main Injector: 150 GeV = 150 x 109 electron volts = 1.5 x 1011
electron volts
Tevatron: 0.98 TeV (Tera electron volts, trillion electron volts) = nearly 1012
electron volts
EXAMPLES of SMALL NUMBERS:
1 centimeter = 1 cm = 10-2
m ~ 2/5 inch width of a pen
1 millimeter = 1 mm = 10-3 m ~ 1/25 inch width
of lead in pencil
1 micrometer = 1 micron = 10-6
High power
microscopes look at objects as small as a few micrometers
1 microsecond = 10-6 seconds
The lifetime of a mu-lepton is
about 2 microseconds
1 nanosecond = 10-9 seconds
A pi-meson lives on the
average for 26 nanoseconds
A particle at the speed of light travels about one foot in one
nanosecond.
In an ordinary coax cable an
electrical pulse travels about 2/3 the speed of light. A cable 18 inches long will
delay an electrical pulse for one nanosecond.
1 nm = 1 nanometer = 10-9 m
1 Å = 1 Ångstrom = 10-10 m
The wavelength of VISIBLE light ranges from about
7000 Å (red) to 4000 Å (violet)
1 Fermi = 10-15 meters
The radius of a proton
is about 1.2 Fermis