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• 1. Course 3, Lesson 1-7 Write each number in standard form. 1. 5.92 × 104 2. 1.9 × 10–6 3. 6.7 × 108 Write each number in scientific notation. 4. 26,400,000 5. 11,000 6. 0.000098 7. The diameter of Jupiter at its equator is approximately 143,000 kilometers. Write this number in scientific notation.
• 2. Course 3, Lesson 1-7 ANSWERS 1. 59,200 2. 0.0000019 3. 670,000,000 4. 2.64 × 107 5. 1.1 × 104 6. 9.8 × 10–5 7. 1.43 × 105
• 3. WHY is it helpful to write numbers in different ways? The Number System Course 3, Lesson 1-7
• 4. Course 3, Lesson 1-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. The Number System • 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other. • 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.
• 5. Course 3, Lesson 1-7 Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. The Number System Mathematical Practices 1 Make sense of problems and persevere in solving them. 3 Construct viable arguments and critique the reasoning of others. 4 Model with mathematics.
• 6. To • add, subtract, multiply and divide with numbers written in scientific notation Course 3, Lesson 1-7 The Number System
• 7. 1 Need Another Example? 2 3 4 5 Step-by-Step Example 1. Evaluate (7.2 × 103)(1.6 × 104). Express the result in scientific notation. (7.2 × 103)(1.6 × 104) = (7.2 × 1.6)(103 × 104) = (11.52)(103 × 104) = 11.52 × 103 + 4 = 11.52 × 107 = 1.152 × 108 Commutative and Associative Properties Multiply 7.2 by 1.6. Product of Powers Add the exponents. Write in scientific notation.
• 8. Answer Need Another Example? Evaluate (1.1 × 10–3)(2.5 × 109). Express the result in scientific notation. 2.75 × 106
• 9. 1 Need Another Example? 2 3 4 5 6 Step-by-Step Example 2. In 2010, the world population was about 6,860,000,000. The population of the United States was about 3 × 108. About how many times larger is the world population than the population of the United States? Estimate the population of the world and write in scientific notation. 6,860,000,000 ≈ 7,000,000,000 or 7 × 109 Find . = ≈ 2.3 × Associative Property Divide 7 by 3. Round to the nearest tenth. Quotient of Powers 7 ≈ 2.3 × 101 So, the population of the world is about 23 times larger than the population of the United States. ≈ 2.3 × 109 – 8 Subtract the exponents.
• 10. Answer Need Another Example? The largest planet in our solar system is Jupiter with a diameter of about 143,000 kilometers. The smallest planet in our solar system is Mercury with a diameter of about 5 × 103 kilometers. About how many times greater is the diameter of Jupiter than the diameter of Mercury? Sample answer: 3 × 101 or 30 times greater
• 11. 1 Need Another Example? 2 3 4 Step-by-Step Example 3. Evaluate the expression. Express the result in scientific notation. (6.89 × 104) + (9.24 × 105) (6.89 × 104) + (9.24 × 105) = (6.89 + 92.4) × 104 Write 9.24 × 105 as 92.4 × 104. Distributive Property Rewrite in scientific notation.= 9.929 × 105 = (6.89 × 104) + (92.4 × 104) = 99.29 × 104 Add 6.89 and 92.4.
• 12. Answer Need Another Example? Evaluate (2.85 × 107) + (1.61 × 109). Express the result in scientific notation. 1.6385 × 109
• 13. 1 Need Another Example? 2 3 4 5 Step-by-Step Example 4. Evaluate the expression. Express the result in scientific notation. (7.83 × 108) – 11,610,000 (7.83 × 108) – (1.161 × 107) = (78.3 × 107) – (1.161 × 107) Rewrite 11,610,000 in scientific notation. Write 7.83 × 108 as 78.3 × 107. Subtract 1.161 from 78.3.= 77.139 × 107 = (78.3 – 1.161) × 107 Distributive Property (7.83 × 108) – (1.161 × 107) Rewrite in scientific notation.= 7.7139 × 108
• 14. Answer Need Another Example? Evaluate (8.23 × 106) – 391,000. Express the result in scientific notation. 7.839 × 106
• 15. 1 Need Another Example? 2 3 4 Step-by-Step Example 5. 593,000 + (7.89 × 106) = (0.593 × 106) + (7.89 × 106) = (5.93 × 105) + (7.89 × 106) Rewrite 593,000 in scientific notation. Write 5.93 × 105 as 0.593 × 106 Add 0.593 and 7.89.= 8.483 × 106 = (0.593 + 7.89) × 106 Distributive Property 593,000 + (7.89 × 106)
• 16. Answer Need Another Example? Evaluate 6,450,000,000 – (8.27 × 107). Express the result in scientific notation. 6.3673 × 109
• 17. How did what you learned today help you answer the WHY is it helpful to write numbers in different ways? Course 3, Lesson 1-7 The Number System
• 18. How did what you learned today help you answer the WHY is it helpful to write numbers in different ways? Course 3, Lesson 1-7 The Number System Sample answer: • It is much easier to multiply or divide very large or very small numbers when they are written in scientific notation.
• 19. Write a short paragraph to describe how yesterday’s lesson on scientific notation helped you with today’s lesson. Ratios and Proportional RelationshipsThe Number System Course 3, Lesson 1-7