In physics and other science, it is often necessary to deal with very large and very small numbers. For example the number of atoms in one cubic centimeter of air is about 10,000,000,000,000,000,000 atoms, while the mass of the hydrogen atom is 0.00000000000000000000000000167 Kg.

Instead of writing and carrying so many zeros, the numbers are usually written as figures between 1 and 10 multiplied by the appropriate power of 10. For example 10,000,000,000,000,000,000 is 1x1019, and the mass of the hydrogen atom given above is written simply as 1.67x10-27.

Additional examples are given below:

One hundredth = 0.01 = 10-2
One tenth = 0.1 = 10-1
One = 1 = 100
Ten = 10 = 101
One hundred = 100 = 102
One thousand = 1000 = 103
One million = 1,000,000 = 106
One billion = 1,000,000,000 = 109
The powers-of-ten notation is not only compact and convenient, it also simplifies arithmetic. To multiply two numbers expressed as powers of ten, you need only add the exponents. And to divide, you subtract the exponents. Here are several examples:


100 X 100,000 = 102 X 105 = 102+5 = 107
0.01 X 1,000,000 = 10-2 X 106 = 106-2 = 104
1,000,000 ÷ 1000 = 106 ÷ 10-3 = 106-3 = 103
100 ÷ 1,000,000 = 102 ÷ 10-6 = 102-6 = 10-4

Speed of light: C = 2.998 X 108 m/s
Light year: LY = 9.46 X 1015 m
Absolute Zero temperature: To = -273°C
Mass of Earth: Me = 6.0 X 1024 kg
Diameter of Earth: De = 1.3 X 107 m
Mass of Sun: Ms = 2.0 X 1030 kg
Diameter of Sun: Ds = 1.4 X 109 m
Age of Universe: Tu = 13 X 109 years
Number of cells in adult human: = 60 X 1012 cells
Number of atoms in one cell: = 120 X 1012 atoms
Number of atoms in one cm3 of air we breathe: = 1019 atoms
 Number of atoms in one cm3 of interstellar gas of the Galaxy: = 1 atom
Number of atoms in one m3 of intergalactic space: = 1 atom
Number of electrons (or protons) in the universe = 1080 electrons
Number of photons in the universe: = 1089 photons