1. Whole Number Arithmetic Rounding and estimating

2. Round to the nearest whole number 621.8 19.02 57.04 98.63 1.03 610.8 519.6 622 19 57 99 1 611 520

3. Round to one decimal place 19.023 57.046 81.774 89.522 1.03 2.59 49.97 19.0 57.0 81.8 89.5 1.0 2.6 50.0

4. Round to two decimal places 1.902 5.704 0.1036 2.974 0.006 3.899 0.003 1.90 5.70 0.10 2.97 0.01 3.90 0.00

5. The reading 4.1 kg, has two significant figures.

6. The width of the footpath is 1.81m (to the nearest cm)

7. How many significant figures?

8. Complete this table Rounded widthSignificant Figures 1.81 2 1

9. Complete this table Rounded widthSignificant Figures 1.813 1.82 21

10. Round to one significant figure 7.56 2.7 4.6 10.6 8 3 5 10

11. How many significant figures? 9.6 2.5 55.1 1.26 22.4 178.3 8.75 3.24 2 2 3 3 3 4 3 3

12. How many significant figures? 46.81 3.808 4.077 71.08 83.881 778.049 4 4 4 4 5 6

13. How many significant figures? 400.00 40.0 1.4 1.40 1.400 10.0 1.50 100.00 5 3 2 3 4 3 3 5

14. The length of this pencil is 83 mm to the nearest mm. 83 mm has been rounded to two significant figures. 83 mm = 0.083 m 0.083 m also has two significant figures.

15. How many significant figures? 0.061 0.007 0.00061 0.46 0.070 0.0700 0.0074 0.07006 2 1 2 2 2 3 2 4

16. Exercise 9 Rounding

17. Round the lengths of N. Z. Rivers to the nearest 10 Km. Waikato Clutha Wanganui Taieri Rangitiki Waitaki 425 322 290 288 241 209

18. Round the lengths of N. Z. Rivers to the nearest 10 Km. Waikato Clutha Wanganui Taieri Rangitiki Waitaki 425 = 430 322 = 320 290 = 290 288 = 290 241 = 240 209 = 210

19. Round the heights of N. Z. Mountains to the nearest 100 m. Cook Tasman Ruapehu Taranaki Ngauruhoe Tongariro 3764 3498 2797 2518 2291 1968

20. Round the heights of N. Z. Mountains to the nearest 100 m. Cook Tasman Ruapehu Taranaki Ngauruhoe Tongariro 3764 = 3800 3498 = 3500 2797 = 2800 2518 = 2500 2291 = 2300 1968 = 2000

21. Round the areas of N. Z. Lakes to the nearest 1000 ha. Taupo Te Anau Wakatipu Wanaka Manapouri Hawea 60 606 34 447 29 267 19 166 14 245 11 914

22. Round the areas of N. Z. Lakes to the nearest 1000 ha. Taupo Te Anau Wakatipu Wanaka Manapouri Hawea 60 606 = 61 000 34 447 = 34 000 29 267 = 29 000 19 166 = 19 000 14 245 = 14 000 11 914 = 12 000

23. Round the areas of N. Z. Regions correct to 2 significant figures. Northland Auckland Waikato Bay of Plenty Gisborne Hawkes' Bay Taranaki Manawatu - Wanganui Wellington 13 941 5 600 25 598 12 447 8 351 14 164 7 273 22 215 8 124

24. Round the areas of N. Z. Regions correct to 2 significant figures. Northland Auckland Waikato Bay of Plenty Gisborne Hawkes' Bay Taranaki Manawatu - Wanganui Wellington 13 941 = 14 000 5 600 = 5 600 25 598 = 26 000 12 447 = 12 000 8 351 = 8 400 14 164 = 14 000 7 273 = 7 300 22 215 = 22 000 8 124 = 8 100

25. Round the population of N. Z. Regions correct to 3 significant figures. Nelson Tasman Marlborough West Coast Canterbury Otago Southland New Zealand 40 279 37 973 38 397 32 512 468 040 185 083 97 100 3 618 302

26. Round the population of N. Z. Regions correct to 3 significant figures. Nelson Tasman Marlborough West Coast Canterbury Otago Southland New Zealand 40 279 = 40 300 37 973 = 38 000 38 397 = 38 400 32 512 = 32 500 468 040 = 468 000 185 083 = 185 000 97 100 = 97 100 3 618 302 = 3 620 000

27. This table shows the population of Auckland's 4 cities rounded to the nearest 1000. Copy down and complete the table. CityPopulationMin. PopMax. Pop North Shore172 000 171 500172 499 Waitakere 156 000 Auckland 346 000 Manukau254 000

28. This table shows the population of Auckland's 4 cities rounded to the nearest 1000. Copy down and complete the table. CityPopulationMin. PopMax. Pop North Shore172 000 171 500172 499 Waitakere 156 000155 500156 499 Auckland 346 000345 500346 499 Manukau254 000253 500254 499

29. Exercise 10 Approximate Calculations

30. Oral examples - 1 a. 90 x 6 b. 90 x 60 c. 900 x 60 d. 900 x 600 540 5400 54 000 540 000

31. Oral examples - 2 a. 80 x 5 b. 80 x 50 c. 800 x 50 d. 800 x 500 400 4000 40 000 400 000

32. Oral examples - 3 = 50

33. Oral examples - 3 = 50

34. Oral examples - 3 = 500

35. Oral examples - 3 = 500

36. Oral examples - 4 = 200

37. Oral examples - 4 = 200

38. Oral examples - 4 = 2000

39. Oral examples - 4 = 2000

40. Written examples 1.80 x 7 2. 80 x 70 3. 800 x 70 4. 800 x700 560 5600 56 000 560 000

41. Written examples 5. 40 x 5 6. 40 x 50 7. 400 x 50 8. 400 x 500 200 2000 20 000 200 000

42. 9. = 50

43. 10. = 50

44. 11. = 500

45. 12. = 500

46. 13. = 200

47. 14. = 20

48. 15. = 2000

49. 16. = 2000

50. Estimation Answers are not exact

51. Exercise 10 17. 91 x 18 18. 82 x 29 19. 73 x 36 20. 64 x 47 21. 621 x 19 22. 685 x 32 23. 817 x 38 24. 893 x 51 90 x 20 ≈ 1800 80 x 30 ≈ 2400 70 x 40 ≈ 2800 60 x 50 ≈ 3000 600 x 20 ≈ 12000 600 x 30 ≈ 18000 800 x 40 ≈ 32000 900 x 50 ≈ 45000

52. 25. ≈ 5

53. 26. ≈ 2

54. 27. ≈ 4

55. 28. ≈ 3

56. 29. ≈ 40

57. 30. ≈ 30

58. 31. ≈ 20

59. 32. ≈ 50

60. 33. ≈ 400

61. 34. ≈ 2500

62. 35. ≈ 90 000

63. 36. ≈ 160 000

64. 37. ≈ 10

65. 38. ≈ 20

66. 39. ≈ 30

67. 40. ≈ 100

68. 41. ≈ 40

69. 42. ≈ 20

70. 43. ≈ 60

71. 44. ≈ 30

72. 45. ≈ 2

73. 46. ≈ 4

74. 47. ≈ 6

75. 48. ≈ 3

76. 49. ≈ 8 000

77. 50. ≈ 27 000

78. 51. ≈ 160 000

79. 52. ≈ 810 000

80. 53. The sun is 150 million kilometres from the earth. Light travels a distance of 300 000 kilometres every second. Find, in seconds, how long it takes light from the sun to reach the earth.

81. 53. The sun is 150 million kilometres from the earth. Light travels a distance of 300 000 kilometres every second. Find, in seconds, how long it takes light from the sun to reach the earth.

82. 54. The earth travels 958 million kilometres in its orbit around the sun each year (365 days). By rounding off each number correct to 1 significant figure calculate how far the earth travels in 1 hour.

83. 54. The earth travels 958 million kilometres in its orbit around the sun each year (365 days). By rounding off each number correct to 1 significant figure calculate how far the earth travels in 1 hour.

84. 55. Repeat question 54 only use a calculator to do the actual calculation. (Round off your answer correct to 2 significant figures.)

85. 55. Repeat question 54 only use a calculator to do the actual calculation. (Round off your answer correct to 2 significant figures.) 110000 km

86. 56. Use a calculator to help you find how many days there are in 1 million seconds. (Round off your answer correct to 3 significant figures.)

87. 56. Use a calculator to help you find how many days there are in 1 million seconds. (Round off your answer correct to 3 significant figures.) 11.6 days

88. Making Estimates Continued

89. Fill the gaps ItemUnit cost ($) QuantityEstimated cost ($) Apples1.834 Chickens8.959 Calculator16.857 DVD9.9510

90. Fill the gaps ItemUnit cost ($) QuantityEstimated cost ($) Apples1.8348 Chickens8.95981 Calculator16.857140 DVD9.9510100

91. Fill the gaps ItemUnit cost ($) QuantityEstimated cost ($) Hairdryer23.1538 Toaster47.9527 Shorts14.8574 Chairs83.7565

92. Fill the gaps ItemUnit cost ($) QuantityEstimated cost ($) Hairdryer23.1538800 Toaster47.95271500 Shorts14.8574700 Chairs83.75655600

93. Fill the gaps ItemTotal costQuantityEstimated unit cost Shorts64.917 Books47.998 Heaters33859 Fridges67257

94. Fill the gaps ItemTotal costQuantityEstimated unit cost Shorts64.9179 Books47.9986 Heaters33859400 Fridges672571000

95. Fill the gaps ItemTotal costQuantityEstimated unit cost Watches222551 Shoes430978 Calculator268392 Trousers341683

96. Fill the gaps ItemTotal costQuantityEstimated unit cost Watches22255140 Shoes43097850 Calculator26839230 Trousers34168340