Transcript Section 2.2
Chapter 2.2 Scientific Notation Scientific Notation • Expresses numbers in two parts: • A number between 1 and 10 • Ten raised to a power • Examples: • 2.32 x 102 • 1.767 x 10-12 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 103 = 4,560 • 1.2 x 105 = 120,000 • 6.8 x 102 = 680 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 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 Example 2,345,000 Expressed as a factor between 1 and 10: 2.345 Decimal moved 6 places to the left: 2.345 x 106 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 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 102 + 3 x 103 = 6 x 102 + 30 x 102 = 36 x 102 = 3.6 x 103 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 Multiplication Example (4 x 103) x (2 x 104) Multiply the first factors 4 x 2= 8 Add the exponents 3+4=7 Combine the factors 8 x 107 Division Example (15 x 103) ÷ (3 x 10-4) Divide the first factors 15 ÷ 3 = 5 Subtract the exponents 3 – (-4) = 7 Combine the factors 5 x 107 Homework • Practice problems 12-21 on pages 32-35