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Scientific Notation THE LOGICAL APPROACH
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Warm Up Write each number in standard notation. 2.54 x 102 6.7 x 102 1.14 x 103 Write each number in scientific notation. 75,000,000 208 907,100
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Positive Exponents 101 = 10 102 = 10X10= 100 103 = 10X10X10 = 1000
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Negative Exponents 10-1 = 1/10 = 0.1 10-2 = 1/100 = 0.01
10-3 = 1/1000 = 0.001 10-4 = 1/10000 =
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Scientific Notation We use the idea of exponents to make it easier to work with large and small numbers. 10,000 = 1 X 104 250,000 = 2.5 X 105 Count places to the left until there is one number to the left of the decimal point. 230,000 = ? 35,000 = ?
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Scientific Notation Continued
= 6 X 10-5 = 4.5 X 10-4 Count places to the right until there is one number to the left of the decimal point 0.003 = ? = ?
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Multiplying with Scientific Notation
Add the Exponents 102 X 103 = 105 100 X 1000 = 100,000
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Multiplying with Scientific Notation
(2.3 X 102)(3.3 X 103) 230 X 3300 Multiply the Coefficients 2.3 X 3.3 = 7.59 Add the Exponents 102 X 103 = 105 7.59 X 105 759,000
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Multiplying with Scientific Notation
(4.6 X 104) X (5.5 X 103) = ? (3.1 X 103) X (4.2 X 105) = ?
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Dividing with Scientific Notation
Subtract the Exponents 104/103 = 101 10000X 1000 = 10
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Dividing with Scientific Notation
(3.3 X 104)/ (2.3 X 102) 33000 / 230 = Divide the Coefficients 3.3/ 2.3 = Subtract the Exponents 104 / 102 = 102 X 102
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Dividing with Scientific Notation
(4.6 X 104) / (5.5 X 103) = ? (3.1 X 103) / (4.2 X 105) = ?
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