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Chapter 2.2 Scientific Notation

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Expresses numbers in two parts: A number between 1 and 10 Ten raised to a power Examples: 2.32 x 10 2 1.767 x 10 -12

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Interpreting Scientific Notation When the power of ten is positive, than the number is larger than 1 Move the decimal to the right Examples: 4.56 x 10 3 = 4,560 1.2 x 10 5 = 120,000 6.8 x 10 2 = 680 When the power of ten is positive, than the number is larger than 1 Move the decimal to the right Examples: 4.56 x 10 3 = 4,560 1.2 x 10 5 = 120,000 6.8 x 10 2 = 680

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Interpreting Scientific Notation When the power of ten is negative, than the number is smaller than 1 Move the decimal to the left Examples: 5.23 x 10 -3 = 0.00523 2.03 x 10 -2 = 0.0203 7 x 10 -5 = 0.000007

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Converting Data into Scientific Notation Move the decimal to produce a factor between 1 and 10 Count the number of places the decimal moved and in what direction If it moved to the left, express the exponent as a positive number If it moved to the right, express the exponent as a negative number

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Example 2,345,000 Expressed as a factor between 1 and 10: 2.345 Decimal moved 6 places to the left: 2.345 x 10 6

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Example 0.00178 Expressed as a factor between 1 and 10: 1.78 Decimal moved 3 places to the right: 1.78 x 10 -3

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Adding and Subtracting Only add and subtract numbers with the same exponent Convert numbers to the same power of ten before adding or subtracting 6 x 10 2 + 3 x 10 3 = 6 x 10 2 + 30 x 10 2 = 36 x 10 2 = 3.6 x 10 3

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Multiplying and Dividing The numbers do not have to have the same exponent For multiplying: Multiply the first factors, then add the exponents For dividing: Divide the first factors, than subtract the exponent of the divisor from the exponent of the dividend

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Multiplication Example (4 x 10 3 ) x (2 x 10 4 ) Multiply the first factors 4 x 2= 8 Add the exponents 3 + 4 = 7 Combine the factors 8 x 10 7

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Division Example (15 x 10 3 ) ÷ (3 x 10 -4 ) Divide the first factors 15 ÷ 3 = 5 Subtract the exponents 3 – (-4) = 7 Combine the factors 5 x 10 7

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Homework Practice problems 12-21 on pages 32-35

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