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Name Class Date Practice 6-1 Scientific Notation Write each number in scientific notation. 1. 45 5. 4,100 All rights reserved. 9. 38,050 2. 250 3.90 6. 500 7.43,200 10. 480,000 4.670 8.97,100 11.900,000 12.8,750,000 Write each number in standard form. 13. 3.1 3 101 17. 2.86 3 105 21. 4.83 3 109 14. 8 3 102 15.4.501 3 104 18. 3.58 3 106 19.8.1 3 101 22. 2.73 3 108 16.9.7 3 106 20.9.071 3 102 23.2 3 105 24.8.09 3 104 © Pearson Education, Inc., publishing as Pearson Prentice Hall. Order each set of numbers from least to greatest. 25. 8.9 3 102, 6.3 3 103, 2.1 3 104, 7.8 3 105 26. 2.1 3 104, 2.12 3 103, 3.46 3 105, 2.112 3 102 27. A mulberry silkworm can spin a single thread that measures up to 3,900 ft in length. Write the number in scientific notation. Write each number in scientific notation. 28. 0.025 29. 0.00003 30.0.00197 31.0.000407 Write each number in standard form. 32. 8.1 3 1023 Practice 441198_C3_Ch6_WKbk_Ver-2.indd 195 33. 3.42 3 1025 34.9.071 3 1026 35.2 3 1024 Course 3 Lesson 6-1 195 10/10/12 4:39 PM Name Class Date Practice 6-2 Exponents and Multiplication Write each expression using a single exponent. 1. 32 ? 35 2.13 ? 14 ? 0.8 All rights reserved. 7. 33 4. 0.83 5. 34 (21.3)2 ? (21.3)4 ?3? 3.(23)12 ? (23)5 8.22 ? 22 ? 22 6. 4.58 ? 4.52 9.5 ? 54 ? 53 Simplify each expression. 10. a1 ? a2 11.m5 ? m 16. 10jk5 13. (3x) ? (3x) 9d8 ? 14.4d ? 3j3k2 12.(2y)3 ? (2y)2 17.2p3q2 ? 3p2q3 15.x2y ? xy2 18.5x2 ? x6 ? x3 © Pearson Education, Inc., publishing as Pearson Prentice Hall. Replace each ? with 5, <, or >. 19. 38 ? 3 ? 37 20.49 ? 72 ? 72 22. A square has a side length of 7x4 21. 53 ? 54 ? 252 in. Find the area of the square. 23. The formula for the volume of a rectangular prism is V 5 ? w ? h. What is the volume of a prism with length 2x2 mm, width 4x mm, and height x3 mm? 24. One meter is equal to 102 centimeters. One kilometer is equal to 103 meters. How many centimeters are in one kilometer? Practice 441198_C3_Ch6_WKbk_Ver-2.indd 197 Course 3 Lesson 6-2 197 10/10/12 4:39 PM Name Class Practice 6-3 Date Multiplying with Scientific Notation Find each product. Write the answers in scientific notation. 1. (3 3 104)(5 3 106) 2. (7 3 102)(6 3 104) 3. (4 3 105)(7 3 108) All rights reserved. 4. (9.1 3 106)(3 3 109) 5. (8.4 3 109)(5 3 107) 6. (5 3 103)(4 3 106) 7. (7.2 3 108)(2 3 103) 8. (1.4 3 105)(4 3 1011) Choose the most reasonable unit to describe the quantity. Then use scientific notation to describe the quantity using the other unit. 9. The mass of a bicycle is about 6 _____. (g, kg) 10. The length of a school bus is 12 _____. (m, km) 11. Double the number 4.6 3 1015. Write the answer in scientific notation. © Pearson Education, Inc., publishing as Pearson Prentice Hall. 12. Triple the number 2.3 3 103. Write the answer in scientific notation. 13. A company manufactures 3.2 3 104 cell phones per month. How many cell phones does it manufacture per year? 14. Yosemite National Park covers about 7.6 3 105 acres. There are about 4.36 3 104 square feet in one acre. How many square feet does the national park cover? Practice 441198_C3_Ch6_WKbk_Ver-2.indd 199 Course 3 Lesson 6-3 199 10/10/12 4:39 PM Name Class Date Practice 6-4 Exponents and Division Simplify each expression. 2. (23)0 1. 822 5. 225 All rights reserved. 4 9. 4 13. 115 4 118 © Pearson Education, Inc., publishing as Pearson Prentice Hall. (3)6 (3)8 4 (4)8 (4)4 9 16. 10 12 10 19.x16 4 x7 12. 80 8 15.2 8.522 11.2 9 18. g g15 17. b12 b4 7.223 14. 7 4 74 10. 86 4 88 4 6. 323 4.180 3.521 20.v20 4 v25 Complete each equation. ? 21. 1 5 3 35 25. ? 22. 2 1 5 22 (2)7 ? 5 28. q 5 q7 27. z 5 z23 z8 ? 24. 2 1 5 (25) 125 ? 10 26. 5 5 55 1 5 10 ? 1,000 ? 23. 1 5 x x2 ? Is each statement true or false? Explain your reasoning. 29. (21)3 5 123 30. 321 ? 321 5 31 31. 22 ? 222 5 1 32. 72 ? (27)3 5 (27)26 Practice 441198_C3_Ch6_WKbk_Ver-2.indd 201 Course 3 Lesson 6-4 201 10/12/12 11:35 AM Name Class Date Practice 6-5 Dividing with Scientific Notation Divide. Write each quotient in scientific notation. 7 1. 6.8 3 10 3.4 3 3 2. 7.3 3 10 4.5 3 106 105 All rights reserved. 101 5 7. 8.2 3 10 8. 6 7 9. 3.4 3 10 9 12 4.3 3 102 7 6. 6.2 3 10 28 5.6 3 10 5 5. 7.9 3 10 2.3 3 103 24 4. 1.9 3 10 3.3 3 5 3. 2.6 3 10 5.1 3 103 Which of the following numbers is greater? 10. 5.2 3 104 or 5.8 3 103 11. 6 3 103 or 8 3 1023 12. 3.42 3 106 or 3.24 3 106 © Pearson Education, Inc., publishing as Pearson Prentice Hall. 13. 8.1 3 1027 or 8.1 3 1028 Estimate how many times the first number is than the second number. 14. 6 3 1012 and 2 3 1010 15. 4 3 109 and 8 3 105 16. The height of the thermosphere is about 2.95 3 105 feet above Earth. There are 5,280 feet in 1 mile. About how many miles above earth is the thermosphere? 17. The speed of light is about 3.0 3 108 m/s. The speed of sound is about 3.4 3 102 m/s. How much faster does light travel than sound? 18. The distance between Los Angeles, California, and Washington, D.C., is 4.3 3 106 m. The distance between New York City, New York, and Washington, D.C., is 3.6 3 105 m. How much farther is Los Angeles from Washington, D.C., than New York City? Practice 441198_C3_Ch6_WKbk_Ver-2.indd 203 Course 3 Lesson 6-5 203 10/16/12 10:06 AM