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Lesson Menu. Main Idea NGSSS 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

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  1. Lesson Menu Main Idea NGSSS 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 Five-Minute Check

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

  3. MA.8.A.6.1 Use exponents and scientific notation to write large and small numbers and vice versa and to solve problems. MA.8.A.6.4 Perform operations on real numbers (including integer exponents, radicals, percents,scientific notation, absolute value, rational numbers, and irrational numbers) using multistep and real world problems. NGSSS

  4. 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

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

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

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

  8. 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

  9. Associative Property ≈ 0.29 × 102Simplify. ≈ 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

  10. 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

  11. 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) × 107Distributive 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

  12. Evaluate (3.78 × 105) + (5.12 × 106). Express the result in scientific notation. A. 8.9 × 1011 B. 5.498 × 105 C. 54.98 × 105 D. 5.498 × 106 Example 4 CYP

  13. 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

  14. Evaluate (7.54 × 105) – (1.22 × 103). Express the result in scientific notation. A. 6.32 × 102 B. 7.5278 × 104 C. 7.5278 × 105 D. 75.278 × 104 Example 5 CYP

  15. Evaluate (3.2 × 106)(2.8 × 102). Express the result in scientific notation. A. 8.96 × 108 B. 8.96 × 1012 C. 6.0 × 1012 D. 896 × 108 Five Minute Check 1

  16. Evaluate . Express the result in scientific notation. A. 2.75 × 102 B. 7.04 × 102 C. 7.04 × 1012 D. 2.75 × 1012 Five Minute Check 2

  17. Evaluate (1.98 × 104) + (3.06 × 106). Express the result in scientific notation. A. 5.04 × 1010 B. 5.04 × 1024 C. 3.0798 × 106 D. 3.0798 × 104 Five Minute Check 3

  18. Evaluate (2.99 × 1012) – (7.28 × 109). Express the result in scientific notation. A. –4.29 × 1012 B. –4.29 × 103 C. 2.9172 × 1012 D. 2.98272 × 1012 Five Minute Check 4

  19. The empty weight of one airplane is 8.35 × 104 pounds, and the empty weight of a second airplane is 3.07 × 105 pounds. What is the difference in the empty weights of these two airplanes? A. 2.235 × 104 pounds B. 2.235 × 105 pounds C. 5.28 × 104 pounds D. 5.28 × 105 pounds Five Minute Check 5

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