# 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

or

384 000 km = 3.84 x 105 km

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 two more examples:

The mass of a hydrogen atom is

1.673 x 10-27 kg

The wavelength of yellow light is about

550 nm = 550 x 10-9 m = 5.5 x 10-7 m

Some of these ideas are contained in the SI units and their prefixes.

milli- means one-thousandth 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 mg = 1 g

1 mg = 10-3 g = 0.001 g

kilo- means a thousand times larger or 1 000 or 103

1 000 g = 103 g = 1 kg

1 g = 10-3 kg = 0.001 kg

1 000 m = 103 m = 1 km

1 m = 10-3 km = 0.001 km

micro- means one-millionth or 0.000 001 or 10-6

1 000 000 µm = 106 µm = 1 m

1 µm = 10-6 m = 0.000 001 m

nano- means one-billionth or 0.000 000 001 or 10-9

1 000 000 000 nm = 109 nm = 1 m

1 nm = 10-9 m = 0.000 000 001 m