Example 1: Multiplication and Division with Scientific Notation Main Idea Example 1: Multiplication and Division with Scientific Notation Example 2: Multiplication and Division with Scientific Notation Example 3: Real-World Example Example 4: Addition and Subtraction with Scientific Notation Example 5: Addition and Subtraction with Scientific Notation Lesson Menu

Compute with numbers written in scientific notation. Main Idea/Vocabulary

Multiplication and Division with Scientific Notation Evaluate (1.1 × 10–3)(2.5 × 109). Express the result in scientific notation. (1.1 × 10–3)(2.5 × 109) = (1.1 × 2.5 )(10–3 × 109) Commutative and Associative Properties = (2.75)(10–3 × 109) Multiply 1.1 by 2.5. = 2.75 × 10–3 + 9 Product of Powers = 2.75 × 106 Add the exponents. Answer: 2.75 × 106 Example 1

Evaluate (3.2 × 104)(1.9 × 10–8). Express the result in scientific notation. B. 5.1 × 10–4 C. 6.08 × 10–4 D. 6.08 × 10–32 Example 1 CYP

Multiplication and Division with Scientific Notation Evaluate . Express the result in scientific notation. Associative Property Divide 7.75 by 2.5. = 3.1 × 106 – (–2) Quotient of Powers = 3.1 × 108 Subtract the exponents. Answer: 3.1 × 108 Example 2

Evaluate . Express the result in scientific notation. B. 3.5 × 10–4 C. 3.5 × 104 D. 3.5 × 1010 Example 2 CYP

PLANETS The largest planet in our solar system is Jupiter with a diameter of about 1.43 × 105 kilometers. The smallest planet in our solar system is Mercury with a diameter of about 4.9 × 103 kilometers. About how many times greater is the diameter of Jupiter than the diameter of Mercury? Example 3

≈ 2.9 × 101 Write 0.29 × 102 in scientific notation. Associative Property ≈ 0.29 × 102 Simplify. ≈ 2.9 × 101 Write 0.29 × 102 in scientific notation. Answer: The diameter of Jupiter is about 2.9 × 101 or 29 times greater than the diameter of Mercury. Example 3

ASTRONOMY The mass of Jupiter is about 1. 90 × 1027 kilometers ASTRONOMY The mass of Jupiter is about 1.90 × 1027 kilometers. The mass of Pluto is about 1.29 × 1022 kilometers. About how many times greater is the mass of Jupiter than the mass of Pluto? A. 1.47 × 101 times greater B. 1.47 × 105 times greater C. 6.1 × 104 times greater D. 6.1 × 105 times greater Example 3 CYP

Addition and Subtraction with Scientific Notation Evaluate (2.85 × 107) + (1.61 × 109). Express the result in scientific notation. (2.85 × 107) + (1.61 × 109) = (2.85 × 107) + (161 × 107) Write 1.61 × 109 as 161 × 107. = (2.85 + 161) × 107 Distributive Property = 163.85 × 107 Add 0.0285 and 1.61. = 1.6385 × 109 Write 163.85 × 107 in scientific notation. Answer: 1.6385 × 109 Example 4

Evaluate (3.78 × 105) + (5.12 × 106). Express the result in scientific notation. B. 5.498 × 105 C. 54.98 × 105 D. 5.498 × 106 Example 4 CYP

Addition and Subtraction with Scientific Notation Evaluate (8.23 × 106) – (6.91 × 105). Express the result in scientific notation. (8.23 × 106) – (6.91 × 105) = (82.3 × 105) – (6.91 × 105) Write 8.23 × 106 as 82.3 × 105. = (82.3 – 6.91) × 105 Distributive Property = 75.39 × 105 Subtract 6.91 from 82.3. = 7.539 × 106 Write 75.39 × 105 in scientific notation. Answer: 7.539 × 106 Example 5

Evaluate (7.54 × 105) – (1.22 × 103). Express the result in scientific notation. B. 7.5278 × 104 C. 7.5278 × 105 D. 75.278 × 104 Example 5 CYP