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Name:__________________________________ th 8 Grade Math 5.3 Homework: Number Classification Period: ____ Each of the following numbers are Rational. Write the number as a fraction (a ratio of two integers, a/b). 3 1. 0 4. 0.8 2. 2 5 3. -√49 3 5. √8 7. -5 6. √20.25 8. 0.22222… Use their decimal expansions to help classify each number as rational or irrational. Justify your answer. 9. 𝜋 = 3.14159… Irrational Decimal expansion does not terminate. 10. √27 12. √18 13. 15. 𝜋 2 18. √6.25 3 3 11. √4 √1 √49 14. √30 16. -18 17. √12 19. 0.1666666… 20. 3.1 5 21. √8 22. 24. 0 25. √169 6 3 3 23. 1.75642689764…. 26. 525 7896 27-46 Place each number in the correct box in the diagram above. -5 7 1 3 4 √12 3 √2 1 −1 2 2.75 0.6666… √1 3 2𝜋 𝜋 -607 2.5454 52 0 𝜋 2 -2.56 3 √8 √36 √1 Use the diagram above to help you determine if each statement is true of false. Explain your reasoning. 47. Negative numbers are always integers. 48. Irrational numbers are never rational. 49. A whole number is always rational. 50. Decimals can be rational or irrational. Use their decimal expansions to help you plot the numbers on the number line. Compare the numbers. Remember that negative numbers get smaller the further you go to the left on the number line. Use the symbols <,=,>. 3 52. 24 56. -1.5 √5 -1.55 53. - √36 -2𝜋 54. 23 57. 3 58. √25 √27 10 3 2 √64 55. 3.333… 59. √16 √2 3 4𝜋 3 Convert the following terminating decimals to fractions. Reduce to lowest terms. 60. 0.35 61. 0.424 62. - 0.13 63. 0.2 Convert each repeating decimal to a fraction a/b. Show all steps. Reduce to lowest terms. 64. 0.4545 … 65. 0.5777… ̅̅̅ 0.04 66. 67. -1.55555… 68. List the first 12 Perfect Squares (without a calculator): 69. List the first 5 Perfect Cubes (without a calculator): Give the decimal equivalent of the following Benchmark Fractions (without a calculator). 70. 74. 1 2 = _____ 71. = _____ 8 75. 1 1 4 = _____ 72. = _____ 4 76. 3 78. √45 is in between _____ & ______ 3 = _____ 73. 3 8 = _____ = _____ 3 77. 7 8 = _____ 1 3 2 79. √20 is in between _____ & ______ 5.3 KEY 1. 0/1 3. -7/1 5. 2/1 7. -5/1 9. GIVEN 11. 2, Rational: It is a Natural Number 13. 1/7, Rational: It can be written as a fraction. 15. 1.57…, Irrational: Decimal does not terminate or repeat. 17. 3.4641…, Irrational: Decimal does not terminate or repeat. 19. Rational, Decimal repeats. 21. 2, Rational: Cube root of a Perfect Cube and 2 is a Natural Number. 23. Irrational: Decimal does not repeat or terminate. 25. 13, Rational, Square root of a Perfect Square and 13 is a Natural Number. 27. -5 is in the Integers Box 29. Square Root of 2 is in the Irrational Box 31. 2.75 is in the Rational Box 33. Square Root of 1 is in the Natural Box 35. 2 pi is in the Irrational Box 37. 7/1 is in the Natural Box 39. Pi is in the Irrational Box 41. 2. 5454 is in the Rational Box 43. 0 is in the Whole Box 45. -2.56 is in the Rational Box 47. False, Some rational numbers are negative and not integers. Ex: -2.56. Irrational numbers can be negative too. 49. True, Rational Numbers can be written as a fraction and whole numbers can be written as a fraction by putting a 1 in the denominator 51. No number 51 53. Greater than 55. Less than 57. Greater than 59. Less than 61. 53/125 63. 1/5 65. 26/45 67. -14/9 69. 1, 8, 27, 64, 125 71. 0.25 73. 0.375 75. 0.75 77. 0.875 79. 2 & 3

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