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2-5 Irrational Numbers Name Date Irrational numbers are not rational numbers. They are numbers that cannot be expressed as quotients of two integers, a , where b ! 0. b Some irrational numbers are: 38 ; " 95 square roots of nonperfect squares 0.3452799. . . , 0.101001000. . . nonterminating and nonrepeating decimals (including #) 0.23233423342323. . . decimals that have a pattern but do not terminate or repeat exactly Find a rational approximate value for On a calculator, press: 38 to the nearest hundredth. 6.164414003. 38 38 ! 6.16. To the nearest hundredth, Classify each number as rational or irrational. 1. 6 2. 0.4321 3. 12 rational 6. 0.245245245. . . rational 11. ("0.3)4 Copyright © by William H. Sadlier, Inc. All rights reserved. 13. 17. "14# rational 21. 0.1234 14. 20 4 irrational irrational 15. 40 9 25 irrational 16 81 rational 20. "0.407 rational rational 24. 1 78 rational irrational irrational 19. 22. 0.454564567. . . 23. 3 25 rational irrational rational 18. rational 9. 0.676776777. . . 10. " 5 13# # irrational 5. (6.3)2 rational rational rational rational 16. "14 8. 0.707 12. 8# 25 irrational 23 7. " 768 rational 4. 25. rational 118 irrational Find a rational approximate value to the given place. Use a calculator. 26. 27. " 34 to the nearest thousandth 19 to the nearest tenth Press 19 4.358898944 to the nearest tenth, 19 ≈ 4.4 28. 5 to the nearest hundredth 3 !5.831 29. 2 to the nearest thousandth 7 0.756 0.75 Lesson 2-5, pages 44–45. Chapter 2 47 For More Practice Go To: Find a rational approximate value to the given place. Use a calculator. 30. " 11 to the nearest tenth —3.316624790 31. Press 11 7 8 to the nearest tenth . 0.9 !3.3 32. 6 to the nearest thousandth 3 33. 19 11 to the nearest thousandth 1.314 0.816 Find one rational and one irrational number between each pair of numbers. Check students’ answers. Possible answers shown. 10 " 102 " 100 11 " 112 " 121 101, 102, . . . , 119, 120 35. 3 and 4 10.5 and 107 37. "2 and "1 3.1 and 38. 20 and !7.5 and ! 50 11 39. 27 5 and !1.4 and ! 2 40. 4 12 and 5 36. "8 and "7 50 42. 3 and 3.5 !12 and !0.010010001. . . 43. George buys 450 tiles. Each tile is 1 foot by 1 foot. Is it possible for George to use exactly 450 tiles to cover the floor of a square room? Explain your answer. 51 7 and 21 41. 0 and " 34 4.75 and 4.606006000. . . 48 and 3.25 and # 44. A square reflecting pool has an area of 183.84 square meters. What is the approximate perimeter of the reflecting pool? s " 183.84 " 13.5587. . . ! 13.56 P " 4(13.56) " 54.24 meters The approximate perimeter is 54.24 m. No; since 450 is irrational, a square room cannot be exactly 450 ft2. Simplify. 3 5 45. ["3(12(12 ) " 23)] !2197 48 Chapter 2 2 46. 5[(25) " (3 • 15 $ 115)] !815 2 3 • (" 12 ) 47. (34 • 45) " 1 $ 10 79 ! 100 Copyright © by William H. Sadlier, Inc. All rights reserved. 34. 10 and 11