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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 10l 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 1 101 10 1 1 0.01 2 102 100 10 2 2 0.02 2 2 102 100 10 0.0 057 5.7 103 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 8.6 105 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