29:011 Notes on scientific notation
In physics we often deal with very small and very large numbers. For example
the speed of light is approximately 300,000,000 m/s. The size of an atom is
roughly 0.0000000001 m. Rather than writing out all of the zeros, we express
these numbers in scientific notation – a decimal number followed by the factor 10
raised to some power. In scientific notation then the speed of light is roughly 3 
108 m/s (or more precisely 2.99  108 m/s. Small numbers (numbers less than 1)
are handled using negative exponents on the 10. The size of the atom would be
written as 1  10-10 m.
Examples:
4, 500,000 = 4.5  106
0.000789 = 7.89  10l 4
numbers greater than 1: expressed as a decimal number x 10positive integer
10 = 101
100 = 10 x 10 = 102
1,000 = 10 x 10 x 10 = 103
1,000,000 = 10x10x10x10x10x10 = 106 (one million)
1,000,000,000 = 109 (one billion)
1,000,000,000,000 = 1012 (one trillion)
2000 = 2 x 1000 = 2 x 103
2500 = 2.5 x 1000 = 2.5 x 103
the number 1 = 100
numbers less than 1: expressed as a decimal x 10negative integer
1
 101
10
1
1
0.01 
 2  102
100 10
2
2
0.02 
 2  2  102
100 10
0.0 057  5.7 103
0.1 
29:011 – Practice problems on scientific notation
1. Express the following numbers in scientific notation.
(a)
(b)
(c)
(d)
(e)
2,530,000
0.0000072
859
0.001
300,000,000
2. Express the following in standard notation.
(a)
(b)
(c)
(d)
7.35  104
8.6  105
1.87  105
6  108
Answers:
1.
(a)
(b)
(c)
(d)
(e)
2.53 x 106
7.2 x 10–6
8.59 x102
1x10-3
3 x 108
2.
(a)
(b)
(c)
(d)
73,500
0.000086
187000
600,000,000