An
order of magnitude is usually considered a power of
10.
Here are some orders of magnitude.
1 one
10 ten
100 hundred
1,000 thousand
1,000,000 million (thousand thousand)
1,000,000,000 billion (thousand million)
1,000,000,000,000 trillion (million million)
For large orders of magnitude, it is convenient to use a number to represent the number of zeros.
1 = 100 one
10 = 101 ten
100 = 102 hundred
1,000 = 103 thousand
1,000,000 = 106 million (thousand thousand)
1,000,000,000 = 109 billion (thousand million)
1,000,000,000,000 = 1012 trillion (million million)
The number of zeros, written in a superscript notation, is called the exponent.
Multiplication is easy with powers-of-ten notation.
101 * 101 = 102 = 100
102 * 102 = 104 = 10,000
103 * 103 = 106 = 1,000,000
To multiply two powers-of-ten numbers, add the number of zeros (exponents).
Note: Multiplication is represented by the asterisk symbol "
*".
To divide two powers-of-ten numbers, subtract the number of zeros (exponents).
104 / 102 = 102 = 10,000 / 100 = 100
103 / 101 = 102 = 1,000 / 10 = 100
For probabilities, negative exponents are used.
100 / 101 = 10-1 = 0.1
100 / 102 = 10-2 = 0.01
100 / 103 = 10-3 = 0.001
100 / 104 = 10-4 = 0.0001
100 / 105 = 10-5 = 0.00001
100 / 106 = 10-6 = 0.000001
