Scientific Notation
In Physics, as in all of Science, we encounter numbers that are incredibly small and others that are incredibly large. We can express this very wide range of numbers by using "Scientific Notation" or "Powers of Ten Notation". You are probably already familiar with this notation.
Any number can be written as a number between 1.00 and 9.99... multiplied by 10 raised to a power. Here are a few examples:
The distance from Los Angeles to New York is about
4 550 km = 4.55 x 103 km
The distance from Earth to our moon is
384 000 000 m = 3.84 x 108 m
The distance from Earth to our Sun is
150 000 000 km = 1.5 x 108 km
The distance from our Sun to Pluto is
5 930 000 000 km = 5.93 x 109 km
Very small numbers are written with negative exponents of ten since
0.001 = 10-3
0.000 001 = 10-6
0.000 000 001 = 10-9
Here are a few more examples:
The mass of a hydrogen atom is
1.673 x 10-27
Some of these ideas are built into the SI units.milli- means one-thousanth or 0.001 or 10-3
1 000 mm = 103 mm = 1 m
1 mm = 10-3 m = 0.001 m
1 000 mg = 103 mm = 1 g
1 mg = 10-3 g = 0.001 g
1 000 g = 103 g = 1 kg
1 g = 10-3 kg = 0.001 kg
1 000 g = 103 g = 1 kg
1 g = 10-3 kg = 0.001 kg
1 000 000 µm = 106 µm = 1 m
1 µm = 10-6 m = 0.000 001 m
1 000 000 000 nm = 109 nm = 1 m
1 nm = 10-9 m = 0.000 000 001 m
(c) Doug Davis, 2002; all rights reserved