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9.4 Scientific Notation Scientific notation is used to write very large and very small numbers in powers of 10. Decimal form Power of 10 Name 1,000,000,000 109 one billion 1,000,000 106 one million 1,000 103 one thousand 100 102 one hundred 10 101 ten 1 100 one .1 10-1 one tenth .01 10-2 one hundredth .001 10-3 one thousandth Form: c 10n where c is a number > 1 and <10 Change Decimals to Scientific Notation: 93,000,000 9.3 ∙ 107 .00000625 6.25 ∙ 10-6 Examples: 2450 = 2.45 x 103 1.78 = 1.78 x 100 0.000722 = 7.22 x 10-4 Scientific Notation to Decimal Form: 2.83 ∙ 105 283,000 1.5 ∙ 10-7 0.00000015 Examples: 1.345 x 102 = 134.5 3.67 x 104 = 36,700 7.8 x 10-1= 0.78 4.103 x 10-5 = 0.00004103 Multiplying Scientific Notation: (3.2 x 106) (4.2 x 104) Combine like terms 3.2 ∙ 4.2 ∙ 106 ∙ 104 Multiply numbers and add exponents 13.44 x 1010 1.344 x 1011 Pull out another positive power of 10, so 1010 + 101 = 1011! Multiplying Scientific Notation: (1.4 x 104) (7.6 x 103) Combine like terms 1.3 ∙ 7.6 ∙ 104 ∙ 103 Multiply numbers and add exponents 10.64 x 107 1.064 x 108 Pull out another positive power of 10, so 107 + 101 = 108! Dividing with Scientific Notation: 4.5 x 10-7 9.0 x 10-4 4.5 x 10-7 9.0 x 10-4 Rewrite as a product of fractions 0.5 ∙ 10-7-(-4) Divide and subtract exponents 0.5 ∙ 10-3 Simplify 5 x 10-4 0.0005 Scientific notation Dividing with Scientific Notation: 1.2 x 10-1 4.8 x 10-4 1.2 x 10-1 4.8 x 10-4 Rewrite as a product of fractions 0.25 ∙ 10-1-(-4) Divide and subtract exponents 0.25 ∙ 103 Simplify 2.5 x 102 250 Scientific notation Homework page 422 #6-26 even, 33-35 Study for 9.1-9.4 quiz Tuesday