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Solution Manual for Mathematics for Electricity and Electronics, 4th Edition

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    Solutions Manual to Accompany MATHEMATICS FOR ELECTRICITY AND ELECTRONICS FOURTH EDITION Arthur D. Kramer

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    Contents CHAPTER 1 Basic Arithmetic 1 Exercise 1.1 Arithmetic Operations 1 Exercise 1.2 Multiplying and Dividing Fractions 1 Exercise 1.3 Adding Fractions 2 Exercise 1.4 Hand Calculator Operations 2 Review Exercises 3 CHAPTER 2 Decimals and Percentages 3 Exercise 2.1 Decimals 3 Exercise 2.2 Percentages 4 Exercise 2.3 Precision and Accuracy 5 Exercise 2.4 Hand Calculator Operations 5 Review Exercises 6 CHAPTER 3 Powers and Roots 6 Exercise 3.1 Powers 6 Exercise 3.2 Powers of Ten 7 Exercise 3.3 Square Roots and Cube Roots 8 Exercise 3.4 Hand Calculator Operations 8 Review Exercises 9 CHAPTER 4 Systems of Measurement 10 Exercise 4.1 Scientific and Engineering Notation 10 Exercise 4.2 Metric System (SI) 11 Exercise 4.3 The U.S. Customary System 12 Exercise 4.4 Hand Calculator Operations 13 Review Exercises 14 CHAPTER 5 Basic Algebra 15 Exercise 5.1 Signed Numbers 15 Exercise 5.2 Algebraic Terms 15 Exercise 5.3 Rules for Exponents 16 Review Exercises 17 CHAPTER 6 Linear Equations 18 Exercise 6.1 Solution of First-Degree Equations 18 Exercise 6.2 Equation Solving Methods 19 Review Exercises 19 CHAPTER 7 Basics of DC Circuits 20 Exercise 7.1 DC Circuits and Ohm’s Law 20 iii

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    Exercise 7.2 Electric Power 21 Review Exercises 22 CHAPTER 8 Multiplying and Factoring Polynomials 22 Exercise 8.1 Multiplying Polynomials 22 Exercise 8.2 Monomial Factors 23 Exercise 8.3 Binomial Factors 24 Exercise 8.4 Second-Degree Equations 24 Review Exercises 25 CHAPTER 9 Algebraic Fractions 26 Exercise 9.1 Reducing Fractions 26 Exercise 9.2 Multiplying and Dividing Fractions 26 Exercise 9.3 Addition of Fractions 27 Exercise 9.4 Equations with Fractions 28 Review Exercises 29 CHAPTER 10 Formulas and Problem Solving 31 Exercise 10.1 Formulas and Literal Equations 31 Exercise 10.2 Problem Solving 32 Review Exercises 33 CHAPTER 11 Series and Parallel DC Circuits 34 Exercise 11.1 Series Circuits 34 Exercise 11.2 Parallel Circuits 35 Exercise 11.3 Series-Parallel Circuits 36 Review Exercises 37 CHAPTER 12 Graphs 39 Exercise 12.1 Rectangular Coordinate System 39 Exercise 12.2 Linear Function 42 Exercise 12.3 Nonlinear Graphs 46 Review Exercises 50 CHAPTER 13 Linear Systems 54 Exercise 13.1 Graphical Solution of Two Equations 54 Exercise 13.2 Algebraic Solution of Two Equations 56 Exercise 13.3 Solution by Determinants 57 Exercise 13.4 Solution of Three Linear Equations 58 Review Exercises 59 CHAPTER 14 Network Analysis 60 Exercise 14.1 Voltage Division 60 Exercise 14.2 Kirchhoff’s Laws 61 Exercise 14.3 Solving Circuits 61 Review Exercises 62 iv • CONTENTS

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    CHAPTER 15 Network Theorems 63 Exercise 15.1 Superposition Theorem 63 Exercise 15.2 Thevenin’s Theorem 64 Exercise 15.3 Norton’s Theorem 66 Review Exercises 67 CHAPTER 16 Trigonometry of the Right Triangle 69 Exercise 16.1 Angles and Triangles 69 Exercise 16.2 Pythagorean Theorem 70 Exercise 16.3 Trigonometric Ratios 70 Review Exercises 71 CHAPTER 17 Trigonometry of the Circle 72 Exercise 17.1 Trigonometric Functions 72 Exercise 17.2 Reference Angles and Special Angles 73 Exercise 17.3 Inverse Functions 73 Review Exercises 74 CHAPTER 18 Alternating Current 75 Exercise 18.1 Alternating Current Waves 75 Exercise 18.2 Root Mean Square Values 77 Exercise 18.3 Frequency and Period 78 Exercise 18.4 Phase Angle 79 Review Exercises 81 CHAPTER 19 Trigonometry of Vectors 82 Exercise 19.1 Vectors and Phasors 82 Exercise 19.2 Law of Sines 83 Exercise 19.3 Law of Cosines 83 Review Exercises 84 CHAPTER 20 Complex Numbers and Phasors 85 Exercise 20.1 The j Operator 85 Exercise 20.2 Complex Numbers 85 Exercise 20.3 Complex Phasors 86 Exercise 20.4 Operations with Complex Phasors 88 Review Exercises 89 CHAPTER 21 Series AC Circuits 90 Exercise 21.1 Inductive Reactance and RL Series Circuits 90 Exercise 21.2 Capacitive Reactance and RC Series Circuits 91 Exercise 21.3 RLC Series Circuits and Resonance 92 Review Exercises 93 CHAPTER 22 Parallel AC Circuits 94 Exercise 22.1 RL Circuits 94 Exercise 22.2 RC Circuits 94 CONTENTS • v

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    Exercise 22.3 Susceptance and Admittance 95 Exercise 22.4 RLC Circuits 96 Exercise 22.5 AC Networks 97 Exercise 22.6 Filters 97 Review Exercises 98 CHAPTER 23 Exponents and Logarithms 99 Exercise 23.1 Fractional Exponents 99 Exercise 23.2 Exponential Functions 100 Exercise 23.3 Common and Natural Logarithms 102 Review Exercises 103 CHAPTER 24 Applications of Logarithms 104 Exercise 24.1 Exponential Equations 104 Exercise 24.2 RC and RL Circuits 105 Exercise 24.3 Power and Gain 106 Exercise 24.4 Bode Plots 107 Review Exercises 116 CHAPTER 25 Computer Number Systems 119 Exercise 25.1 Binary Number System 119 Exercise 25.2 Binary Arithmetic 119 Exercise 25.3 Octal Number System 120 Exercise 25.4 Hexadecimal Number System 121 Exercise 25.5 Hexadecimal Arithmetic 121 Exercise 25.6 Computer Codes 122 Review Exercises 122 CHAPTER 26 Boolean Algebra 124 Exercise 26.1 Boolean Algebra 124 Exercise 26.2 Logic Circuits 125 Exercise 26.3 Karnaugh Maps 126 Review Exercises 127 CHAPTER 27 Statistics 128 Exercise 27.1 Mean, Median, and Mode 128 Exercise 27.2 Standard Deviation 129 Exercise 27.3 Histograms and the Normal Curve 130 Review Exercises 132 vi • CONTENTS

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    Detailed solutions are shown for more difficult problems. For a group of similar problems, procedures are shown for the first one in the group and for any others that differ significantly. CHAPTER 1 Basic Arithmetic Exercise 1.1 Arithmetic Operations 1. 16 2. 15 3. 4 4. 20 5. 120 6. 160 7. 4 8. 57 9. 36 10. 7 11. 40 12. 5 13. 50 14. 2 15. 26 16. 14 17. 77 18. 9 19. 45 20. 200 21. 10 22. 250 23. 2 24. 30 25. 120 26. 40 27. 5 28. 5 29. 25 30. 9 31. 1 32. 1 33. 10 34. 19 35. 55 36. 150 37. 1500 38. 510 39. 1 40. 5 41. 3 42. 5 43. 180 90 = 20 mi/gal; 210 10 = 21 mi/gal 44. tech $640 40 = $16/hr; teacher $570 30 = $19/hr 45. (6000)(9000) = 54,000,000 mi 46. 44 2 km h = 22 km/h 47. 1 A 48. 2 A 49. 16 V 50. 12 V 51. 7 52. 122 Exercise 1.2 Multiplying and Dividing Fractions 1. 3 5 2. 1 3 3. 4 5 4. 1 2 5. 3 4 6. 2 3 7. 1 5 8. 1 20 9. 2 9 10. 3 7 11. 2 11 12. 6 13 13. 9 35 14. 1 7 15. 2 15 16. 1 24 17. 4 15 18. 11 60 19. 4 3 20. 6 21. 2 22. 5 23. 2 5 24. 1 12 25. 28 45 26. 10 11 27. 2 28. 1 45 29. 5 16 30. 11 12 31. 5 6 32. 5 21 33. 2 21 34. 1 8 35. 6 36. 3 37. 1 3 38. 1 5 39. 1 2 40. 2 5 41. 8 42. 5 14 43. 6 44. 3 2 1

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    45. 1 46. 4 47. 15 50 3 10 = ft 48. 3 4 100 ( ) = 75 ft 49. ( ) 1000 3 5 1 2             = $300 50. ( , ) $ 40 000 1 2 1 4 5000             = 51. 27 V 52. 60 V 53. 1 16 A 54. 1 50 A 55. 9 25 W 56. 1 20 W Exercise 1.3 Adding Fractions 1. 7 7 = 1 2. 4 5 3. 5 8 4. 5 6 5. 13 20 6. 11 14 7. 19 24 8. 11 12 9. 14 15 10. 2 5 11. 31 60 12. 31 36 13. 57 200 14. 41 75 15. 1 4 16. 1 10 17. 1 6 18. 1 60 19. 9 10 20. 7 8 21. 11 20 22. 1 20 23. 85 24 24. 69 35 25. 5 26. 3 4 27. 33 80 28. 37 100 29. 127 200 30. 49 120 31. 7 20 32. 7 100 33. 63 100 34. 15 4 35. 31 60 36. 7 24 37. 2 3 38. 5 6 39. 7 12 40. 6 25 41. 1 80 42. 59 100 43. 13 12 44. 3 20 45. 14 15 46. 3 8 47. 41 100 48. 1 50 49. 11 20 50. 3 4 51. 3 8 52. 1 4 53. 33 40 54. 2 5 55. 1 lb 56. up 5 8 lb 57. 1 4 58. 1 8 59. 13 4 in 60. ( ) ( ) 5 3 6 1 2 5 1 ft in in ft −             ÷ = 61. 10 Ω 62. 25 Ω 63. 20 Ω 64. 300 Ω 65. 20 3 Ω 66. 40 3 Ω 67. 1 10 3 1 2 20 3       ÷                   = 4 68. 7 10 9 10 9 20 7 20       = Exercise 1.4 Hand Calculator Operations 1. 4 2. 197 3. 47 4. 1900 5. 130 6. 12 7. 412 8. 4 9. 2 2 • CHAPTER 1 Basic Arithmetic

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    10. 3 11. 147 12. 32 13. 60 14. 3 15. 40 16. 200 17. 1 18. 2 19. 1 20. 1 21. 4 22. 2 23. 12 24. 1 25. 710 (OIL) 26. 142857 27. 666.7 Ω 28. 57.1 Ω Review Exercises 1. 22 2. 47 3. 12 4. 400 5. 21 6. 135 7. 15 4 8. 1 2 9. 3 2 10. 2 5 11. 15 2 12. 1 9 13. 4 14. 10 15. 5 2 16. 4 5 17. 11 16 18. 1 50 19. 1 5 20. 17 6 21. 2 22. 2 23. 7 24 24. 13 40 25. 5 36 26. 25 27. 27 100 28. 1 28 29. 8 7 30. 7 16 31. 200 32. 58 33. 147 34. 2 35. 2 36. 3 37. 25 mi/h 38. $160 39. 1 2 500       = ( ) 250 ft 40. 500 − 400 − 25 = $75 41. 1000 + 250 = $1250 42. 7 15 4 5 12 16 3 8 −       ÷       ÷ = ft 43. 1 2 A 44. 1 16 A 45. 10 V 46. 24 5 V 47. 18 5 W 48. 24 W 49. 27 V 50. 2 5 A 51. 20 Ω 52. 60 Ω 53. 20 Ω 54. 37 Ω 55. 1 5 5 3 5 5 3 25 9 ÷             = 56. e je j 7 20 1 2 9 10 7 36 = CHAPTER 2 Decimals and Percentages Exercise 2.1 Decimals 1. 10.09 2. 65.129 3. 0.91 4. 69.384 5. 22.71 6. 7.39 7. 4.05 8. 1.202 9. 0.0062 10. 10.01 11. 12 12. 0.069 Exercise 2.1 Decimals • 3

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    13. 6.25 14. 0.02804 15. 0.00001 16. 0.00006 17. 30 18. 210 19. 0.12 20. 33.01 21. 10 22. 0.1 23. 0.08 24. 2.8 25. 32 26. 50 27. 0.8 28. 1.612 29. 12.3 30. 0.87 31. 0.02 32. 0.15 33. 4 34. 0.121 35. 10 36. 1000 37. 40 38. 0.55 39. 7 40. 0.3 41. 0.08 42. 0.4 43. 0.2083 mm 44. 3.12 cm 45. 0.5555 cm 2 46. 0.08 in, 0.0004 in 2 47. 8.4 ft 48. 109.72 m 49. 40.1 V 50. 1.50 A 51. 17.0 cm 52. 4.4 mm, 1.21 mm 2 Exercise 2.2 Percentages 1. 0.75, 75% 2. 0.5, 50% 3. 0.4, 40% 4. 0.3, 30% 5. 0.375, 37.5% 6. 0.875, 87.5% 7. 0.04, 4% 8. 0.09, 9% 9. 0.5625, 56.25% 10. 0.15, 15% 11. 15%, 3 20 12. 25%, 1 4 13. 10%, 1 10 14. 60%, 3 5 15. 12%, 3 25 16. 16%, 4 25 17. 28%, 7 25 18. 36%, 9 25 19. 1 5 , 0.2 20. 4 5 , 0.8 21. 3 20 , 0.15 22. 7 20 , 0.35 23. 43 50 , 0.86 24. 11 20 , 0.55 25. 99 100 , 0.99 26. 49 100 , 0.49 27. 0.05, 5% 28. 0.12, 12% 29. 1.25, 125% 30. 2.4, 240% 31. 1 20 , 5% 32. 2 25 , 8% 33. 3 2 , 150% 34. 1 1 , 100% 35. 6 5 , 1.2 36. 2 1 , 2.0 37. 7 125 , 0.056 38. 101 200 , 0.505 39. 33%, 0.33 40. 0.0625, 6.25% 41. 3 16 , 18.75% 42. 7 8 , 87.5% 43. 17 200 , 0.085 44. 1 16 , 0.0625 45. 1 1000 , 0.1% 46. 0.002, 0.2% 47. 3 48. 16 49. 15 50. 30 51. 1.35 52. 1.19 53. 75 54. 12.5 55. 81 56. 12 57. 1.65 58. 0.4875 59. 2.5 60. 3.625 61. $13.20 62. $150.00 63. 0.95 ft 3 64. 30 g 65. 85% 66. 0.025% 67. $38.00, $42.75 68. $44.00 69. $64.00, $68.80 70. $20.00, $21.65 71. $42.00, $44.10 72. $642 73. 12% 74. 20% 75. 110%, 1120 1000 , 9 8 , 1 1 6 , 1.19 76. 0.03, 1 40 , 0 5 25 . , 0.50% 77. 165 Ω 78. 532 Ω 79. 0.11 A, 1.21 A 80. 0.22 A, 0.88 A 81. 40% decrease 82. 50% increase 83. 20% increase 84. 25% decrease 4 • CHAPTER 2 Decimals and Percentages

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    Exercise 2.3 Precision and Accuracy 1. 3 2. 3 3. 2 4. 2 5. 3 6. 4 7. 3 8. 1 9. 4 10. 1 11. 4 12. 3 13. 4 14. 1 15. 4 16. 3 17. 4 18. 2 19. 2 20. 4 21. 4 22. 3 23. 5, 5.2, 5.15 24. 3, 3.1, 3.10 25. 300, 320, 318 26. 100, 120, 121 27. 0.4, 0.44, 0.445 28. 0.4, 0.44, 0.440 29. 10,000, 9900, 9910 30. 10,000, 11,000, 10,900 31. 80,000, 82,000, 81,900 32. 1000, 1100, 1070 33. 100 100 101 , , 34. 30, 29, 29.0 35. 20, 19, 18.9 36. 0.09, 0.090, 0.0899 37. 20 20 20 0 , , . 38. 40, 39, 39.1 39. 300, 340, 336 40. 500, 450, 454 41. 300 260 260 , , 42. 700, 680, 678 43. 1000 1000 999 , , 44. 9000, 8900, 8890 45. 461 m 2 46. 5,570,000 m 3 47. 152 lb 48. 27.1 ft/s, 18.5 mi/h 49. 18 V 50. 30 mA 51. 203 in 2 52. 0.046 cm 3 53. 120 V 54. 0.11 A 55. 1480 W 56. (a) 1.3 Ω (b) 1.28 Ω 57. (a) $43 (b) $46 58. (a) $170 (b) $172 Exercise 2.4 Hand Calculator Operations 1. 2 2. 8280 3. 21.1 4. 950 5. 2.0 6. 3 7. 0.5 8. 2.5 9. 147 10. 48.4 11. 2.4 12. 0.20 13. 0.68 14. 0.00844 15. 0.143 16. 0.75 17. 0.860 18. 2.69 19. 35.5 20. 124 21. 1.90 22. 167,000 23. 110 24. 505 25. 8.27 26. 0.0270 27. 0.00482 28. 0.000900 29. 0.00266 30. 20.7 31. 197,000,000 mi 2 32. 14.9 cm 33. (a) 4.67% (b) 19.1% 34. ( , )( . ) ( , )( . ) $ , . 87 000 0153 7 850 0 029 13 538 65 + = 35. 33.0 V 36. 295 V 37. 0.415 A 38. 0.338 A Exercise 2.4 Hand Calculator Operations • 5

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    Review Exercises 1. 31.26 2. 0.0011 3. 4.04 4. 8.464 5. 220.1 6. 30 7. 0.25 8. 4 9. 0.006 10. 0.144 11. 20 12. 0.025 13. 44 14. 0.01 15. 0.8, 80% 16. 0.125, 12.5% 17. 0.15, 15% 18. 3 10 , 30% 19. 4 25 , 16% 20. 2, 200% 21. 7 20 , 0.35 22. 1 8 , 0.125 23. 11 200 , 0.055 24. 9 1000 , 0.9% 25. 0.005, 0.5% 26. 3 2 , 1.5 27. 1 28. 8 29. 8.4 30. 24.5 31. 39 32. 0.9 33. 82.5 34. 8.55 35. 0.5 36. 51 37. 33 38. 3.4 39. 0.95 40. 0.058 41. 31.0 42. 0.867 43. 66.9 44. 149 45. 25.3 in, 26.7 in 2 46. $1317.50, $1240.00 47. (40,000)(0.4) e j 3 4 = $12,000 48. (317)(10)(0.75) = 2380 Btu/h 49. $59.84, $64.33 50. $110 51. 76 52. 0.0048 s 53. (a) 0.41 A (b) 2.5 A 54. 210 Ω 55. 10% 56. 33% 57. (4700) e j 1 3 (0.75) = 1175 ≈ 1200 Ω 58. 0.41 A 59. 21 mA 60. (a) 5 15 100 ( %) = 33% (b) 2 5 167 2 3 . . / e j = ≈ 1.7 Ω CHAPTER 3 Powers and Roots Exercise 3.1 Powers 1. 81 2. 64 3. 128 4. 125 5. 100,000 6. 625 7. 121 8. 8000 9. 1 16 , 0.0625 10. 27 1000 , 0.027 11. 9 25 , 0.36 12. 1 125 , 0.008 13. 1 10 000 , , 0.0001 14. 49 100 , 0.49 15. 25 16 , 1.5625 16. 81 625 , 0.1296 17. 0.36, 9 25 18. 0.008, 1 125 19. 2.25, 9 4 20. 36 25 , 1.44 21. 8 125 , 0.064 22. 1 8 , 0.125 23. 0.0001, 1 10 000 , 24. 1 625 , 0.0016 25. 0.000008, 1 125 000 , 26. 0.027, 27 1000 27. 1 9 , 0.111 … 28. 50 29. 1 30. 7 5 , 1.4 31. 1 40 , 0.025 6 • CHAPTER 3 Powers and Roots

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    32. 12 5 , 2.4 33. 6 125 , 0.048 34. 1 4 , 0.25 35. 1 8 , 0.125 36. 67 1000 , 0.067 37. 1 20 , 0.05 38. 11 100 , 0.11 39. 25 8 , 3.125 40. 144 25 , 5.76 41. 9 50 , 0.18 42. 729 100 , 7.29 43. 1 500 , 0.002 44. 8 25 , 0.32 45. 5 64 = 0.078125 46. 3 125 , 0.024 47. 17 250 , 0.068 48. 21 20 , 1.05 49. 75 4 , 18.75 50. 209 4 , 52.25 51. 1 9 , 0.111 … 52. 1 16 , 0.0625 53. 0.512 cm 3 54. 8100 ft 2 55. $26,620 56. $140.26 57. 2.25 mm 2 58. 0.396 ft 3 59. 20 Ω 60. 125 Ω 61. 17 W 62. 50.7 W 63. 0.06 W 64. 18 W Exercise 3.2 Powers of Ten 1. 10 3 2. 10 6 3. 10 0 4. 10 9 5. 10 6 − 6. 10 3 − 7. 10 4 − 8. 10 1 − 9. 10 2 − 10. 10 5 − 11. 10 1 − 12. 10 3 − 13. 10 3 − 14. 10 4 − 15. 100,000 16. 100,000,000 17. 1,000,000 18. 1 19. 0.01, 1 100 20. 0.0001, 1 10 000 , 21. 0.1, 1 10 22. 0.001, 1 1000 23. 0.000001, 1 1 000 000 , , 24. 0.000000001, 1 1 000 000 000 , , , 25. 10 26. 1000 27. 10 6 28. 10 9 29. 10 5 − 30. 10 10 − 31. 10 6 − 32. 10 1 − 33. 10 9 34. 10 6 35. 10 9 − 36. 10 0 37. 10 3 38. 10 4 39. 10 − 2 40. 10 − 5 41. 10 1 = 10 42. 10 2 43. 10 − 2 44. 10 − 6 45. 10 2 46. 10 6 − 47. 10 1 − 48. 10 4 − 49. 10 4 50. 10 7 51. 10 2 52. 10 0 = 1 53. 10 3 − 54. 10 1 ° = 55. 10 9 56. 10 − 6 57. 10 1 − 58. 10 8 − 59. 12 × 10 2 60. 49 × 10 0 = 49 61. 24 × 10 1 = 24 × 10 62. 72 × 10 2 63. 6 × 10 − 12 64. 45 × 10 4 − 65. 12 × 10 1 − 66. 4 × 10 6 67. 3 × 10 3 68. 5 × 10 3 − Exercise 3.2 Powers of Ten • 7

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    69. 2.5 × 10 7 70. 5 10 7 × 71. 2.5 × 10 2 − 72. 4.5 × 10 5 73. 0.75 × 10 6 74. 1 × 10 5 75. 16 × 10 3 , 16,000 76. 40 × 10 6 − , 0.000040 77. 7 × 10 9 − , 0.000000007 78. 5 × 10 12 , 5,000,000,000,000 79. 6.5 × 10 4 , 65 × 10 3 , 65,000 80. 6 × 10 3 = 60 × 10 2 = 6000 81. 29 × 10 4 − = 2.9 × 10 3 − , 0.0029 82. 43 × 10 − 2 = 4.3 × 10 1 − , 0.43 83. 4.5 × 10 = 45 84. 0 85. 480 W 86. 3.8 W 87. 45.5 A 88. 100 A 89. 3.0 V 90. 0.0099 V 91. 0.05 A 92. 0.11 A 93. 2000 Ω 94. 300,000 Ω Exercise 3.3 Square Roots and Cube Roots 1. 4 2. 11 3. 5 2 4. 3 10 5. 2 3 6. 2 9 7. 0.8 8. 0.6 9. 0.1 10. 0.3 11. 200 12. 50 13. 30 14. 40 15. 0.09 16. 0.12 17. 1.3 18. 1.5 19. 3 20. 5 21. 1 2 22. 2 5 23. 0.1 24. 0.2 25. 10 26. 0.1 27. 14 28. 18 29. 28 30. 24 31. 1.4 32. 2.2 33. 2.1 34. 1.8 35. 12 36. 18 37. 0.6 = 3 5 38. 0.04 = 1 25 39. 2 40. 1 5 = 0.2 41. 0.1 = 1 10 42. 1 2 = 0.5 43. 64 × 10 9 44. 36 × 10 4 45. 16 × 10 8 46. 27 × 10 12 47. 0.64 × 10 10 48. 0.01 × 10 2 49. 0.001 × 10 9 50. 0 008 10 18 . × 51. 9 × 10 11 52. 32 × 10 10 53. 150 × 10 6 54. 0 2 10 14 . × 55. 4 × 10 3 56. 5 × 10 2 57. 12 × 10 58. 7 × 10 6 59. 0.5 × 10 2 60. 0.8 × 10 3 61. 2 × 10 3 62. 3 × 10 63. 6 × 10 3 64. 5 × 10 4 65. 0.2 × 10 1 66. 0.5 × 10 1 − 67. 1.5 × 10 5 − 68. 0.32 × 10 2 − 69. 0.75 × 10 5 70. 4 × 10 2 71. 70 ft 72. 100 mm, 10 cm 73. 3% 74. 4% 75. 2.5 76. 0.1 ft 77. 20 Ω 78. 25 Ω 79. 60 V 80. 0.02 A 81. 0.2 A 82. 48 V 83. 6.4 W 84. 7.2 W 85. 0.05 A 86. 400 V 87. 16 9 2 9 2 + = 88. 4(9) − 11 = 25 Exercise 3.4 Hand Calculator Operations 1. 58.1 2. 0.885 3. 0.0101 4. 56.6 5. 0.655 6. 0.0364 7. 79.7 8. 8.95 8 • CHAPTER 3 Powers and Roots

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    9. 0.242 10. 2.95 11. 57.0 12. 0.202 13. 15.0 14. 0.940 15. 10.1 16. 0.606 17. 57.4 18. 2.19 19. 97.9 20. 2.74 21. 148 cm 3 22. 341 m/s 23. 0.794 W 24. 1320 W 25. 4830 Ω 26. 9 66 10 3 . × Ω Review Exercises 1. 343 2. 121 3. 1 16 , 0.0625 4. 8 125 , 0.064 5. 0.216, 27 125 6. 0.064, 8 125 7. 1.21, 121 100 8. 0.001, 1 1000 9. 0.01, 1 100 10. 0.625, 5 8 11. 2 5 , 0.4 12. 0.004, 1 250 13. 1 14. 1 8 , 0.125 15. 0.29, 29 100 16. 0.0625, 1 16 17. 7 18. 6 5 , 1.2 19. 2 5 , 0.4 20. 2 21. 0.3, 3 10 22. 0.11, 11 100 23. 4 24. 0.3, 3 10 25. 1 26. 13 27. 0.06, 3 50 28. 0.9, 9 10 29. 7 30. 11 31. 7 5 , 1.4 32. 0.9, 9 10 33. 100,000,000 34. 0.00001, 1 100 000 , 35. 1 10 000 , , 0.0001 36. 10 3 = 1000 37. 10 2 = 100 38. 10 6 − = 0.000001, 1 1 000 000 , , 39. 10 4 = 10,000 40. 10 4 − = 0.0001, 1 10 000 , 41. 10 5 − = 0.00001, 1 100 000 , 42. 10 1 − = 0.1, 1 10 43. 10 9 = 1,000,000,000 44. 10 01 1 1 10 − = . , 45. 10 6 = 1,000,000 46. 10 6 − = 0.000001, 1 1 000 000 , , 47. 14 × 10 2 48. 24 × 10 8 − 49. 2 × 10 3 − 50. 4.5 × 10 1 − 51. 010 10 10 10 9 10 . . × = × − − 52. 2.5 × 10 0 = 2.5 53. 1 × 10 8 54. 10 55. 16 × 10 5 56. 1 × 10 6 − 57. 6.5 × 10 3 = 65 × 10 2 58. 12 × 10 6 − = 120 × 10 7 − 59. 81 × 10 8 60. 6.75 × 10 6 61. 9 × 10 3 62. 0.6 × 10 63. 4 × 10 3 64. 0.2 × 10 2 65. 7 × 10 3 66. 9 × 10 2 67. 0.1 × 10 7 68. 0.8 × 10 2 69. 0.0140 70. 0.0301 71. 277 72. 0.308 73. 51.7 74. 0.136 75. 9.48 76. 0.326 77. 56 ft 78. $102.50 79. 50 mm = 5 cm 80. 0.216 m 3 81. 50 Ω Review Exercises • 9

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    82. 256 W 83. 0.04 A 84. 20 × 10 2 = 2000 Ω 85. 6.5 Ω 86. 22 V 87. 0.075 × 10 3 = 75 W 88. 0.013 A 89. 0.0031 Ω 90. 0.15 CHAPTER 4 Systems of Measurement Exercise 4.1 Scientific and Engineering Notation 1. 4.26 × 10 10 , 42.6 × 10 9 2. 1.17 × 10 7 , 11.7 × 10 6 3. 9.30 × 10 4 − , 930 × 10 6 − 4. 3.01 × 10 5 − , 30.1 × 10 6 − 5. 1.05 × 10 7 , 10.5 × 10 6 6. 4.49 × 10 4 , 44.9 × 10 3 7. 4.56 × 10 1 , 45.6 × 10 0 8. 2.70 × 10 1 , 27.0 × 10 0 9. 2.35 × 10 0 10. 8.73 × 10 0 11. 1.17 × 10 3 − 12. 9.81 × 10 − 2 , 98.1 × 10 3 − 13. 3.34 × 10 2 , 334 × 10 0 14. 6.99 × 10 4 , 69.9 × 10 3 15. 1.12 × 10 1 − , 112 × 10 3 − 16. 4.09 × 10 1 − , 409 × 10 3 − 17. 1 × 10 3 18. 1 × 10 1 19. 1.62 × 10 5 , 162 × 10 3 20. 7.76 × 10 3 21. 56,400,000, 5.64 × 10 7 , 56.4 × 10 6 22. 336 3 36 10 336 10 2 0 , . , × × 23. 1,200,000, 1.2 × 10 6 24. 14 000 000 1 4 10 14 10 7 6 , , , . , × × 25. 0.000000114, 1.14 × 10 − 7 , 114 × 10 − 9 26. 0 345 3 45 10 34 5 10 2 3 . , . , . × × − − 27. 52.8, 5.28 × 10 1 , 52.8 × 10 0 28. 0 384 384 10 384 10 1 3 . , . , × × − − 29. 0.00569, 5.69 × 10 − 3 30. 1560 1560 10 0 . , . × 31. 5,660,000, 5.66 × 10 6 32. 9 900 000 000 9 90 10 9 , , , , . × 33. 0.000552, 5.52 × 10 − 4 , 552 × 10 − 6 34. 0 0891 8 91 10 891 10 2 3 . , . , . × × − − 35. 26,400,000, 2.64 × 10 7 , 26.4 × 10 6 36. 433 000 4 33 10 433 10 5 3 , , . , × × 37. 0.00000390, 3.90 × 10 − 6 38. 0 0000931 9 31 10 931 10 5 6 . , . , . × × − − 39. 1.45, 1.45 × 10 0 40. 46 7 46 7 10 0 . , . × 41. 0.0101, 1.01 × 10 − 2 , 10.1 × 10 − 3 42. 0 0634 6 34 10 63 4 10 2 3 . , . , . × × − − 43. 112,000, 1.12 × 10 5 , 112 × 10 3 44. 87 000 8 70 10 87 0 10 4 3 , , . , . × × 45. 0.0000105, 1.05 × 10 − 5 , 10.5 × 10 − 6 46. 0 717 717 10 717 10 1 3 . , . , × × − − 47. 871,000,000, 8.71 × 10 8 , 871 × 10 6 48. 4 440 000 4 44 10 6 , , , . × 49. 1.23, 1.23 × 10 0 50. 0 000001005 1005 10 6 . , . × − 51. 125,000, 1.25 × 10 5 , 125 × 10 3 52. 0 0000101 101 10 101 10 5 6 . , . , . × × − − 53. 0.503, 5.03 × 10 − 1 , 503 × 10 − 3 54. 0 0550 5 50 10 55 0 10 2 3 . , . , . × × − − 55. 1.29 × 10 7 , 12.9 × 10 6 , 12,900,000 56. 5 68 10 5 680 000 6 . , , , × 10 • CHAPTER 4 Systems of Measurement

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