Rounding 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 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 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 The reading 4.1 kg, has two significant figures. The width of the footpath is 1.81m (to the nearest cm) How many significant figures? The width of the footpath is 1.81m (to the nearest cm) Complete this table Rounded width Significant Figures 1.81 2 1 Complete this table Rounded width Significant Figures 1.81 3 1.8 2 2 1 Round to one significant figure • • • • 7.56 2.7 4.6 10.6 • • • • 8 3 5 10 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 How many significant figures? • • • • • • 46.81 3.808 4.077 71.08 83.881 778.049 • • • • • • 4 4 4 4 5 6 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 • 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. 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 Exercise 9 Rounding Round the lengths of N. Z. Rivers to the nearest 10 Km. • • • • • • Waikato Clutha Wanganui Taieri Rangitiki Waitaki • • • • • • 425 322 290 288 241 209 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 Round the heights of N. Z. Mountains to the nearest 100 m. • • • • • • Cook Tasman Ruapehu Taranaki Ngauruhoe Tongariro • • • • • • 3764 3498 2797 2518 2291 1968 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 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 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 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 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 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 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 This table shows the population of Auckland's 4 cities rounded to the nearest 1000. Copy down and complete the table. City North Shore Population Min. Pop 172 000 Waitakere 156 000 Auckland 346 000 Manukau 254 000 171 500 Max. Pop 172 499 This table shows the population of Auckland's 4 cities rounded to the nearest 1000. Copy down and complete the table. City North Shore Population Min. Pop 172 000 Max. Pop 171 500 172 499 Waitakere 156 000 155 500 156 499 Auckland 346 000 345 500 346 499 Manukau 254 000 253 500 254 499 Exercise 10 Approximate Calculations 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 Oral examples - 2 • • • • a. b. c. d. 80 x 5 80 x 50 800 x 50 800 x 500 • • • • 400 4000 40 000 400 000 Oral examples - 3 400 8 = 50 Oral examples - 3 4000 = 50 80 Oral examples - 3 40000 = 500 80 Oral examples - 3 400000 = 500 800 Oral examples - 4 800 4 = 200 Oral examples - 4 8000 40 = 200 Oral examples - 4 80000 40 = 2000 Oral examples - 4 800000 400 = 2000 Written examples 1. 2. 3. 4. 80 x 7 80 x 70 800 x 70 800 x700 • • • • 560 5600 56 000 560 000 Written examples 5. 6. 7. 8. 40 x 5 40 x 50 400 x 50 400 x 500 • • • • 200 2000 20 000 200 000 9. 300 6 = 50 10. 3000 = 50 60 11. 30000 = 500 60 12. 300000 = 500 600 13. 600 3 = 200 14. 600 30 = 20 15. 60000 30 = 2000 16. 600000 300 = 2000 Estimation Answers are not exact 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 25. 513 106 ≈5 26. 124 54 ≈2 27. 196 48 ≈4 28. 586 192 ≈3 29. 786 19 ≈ 40 30. 604 21 ≈ 30 31. 597 28 ≈ 20 32. 4253 ≈ 50 82 33. 18 ( ) ≈ 400 2 34. 51 ( ) 2 ≈ 2500 35. ≈ 90 000 302 ( ) 2 36. (389) 2 ≈ 160 000 37. 104 ≈ 10 38. 396 ≈ 20 39. 915 ≈ 30 40. 9810 ≈ 100 41. 78 ´ 21 37 ≈ 40 42. 64 ´ 29 93 ≈ 20 43. 91´ 38 59 ≈ 60 44. 39 ´ 62 81 ≈ 30 45. 82 ´ 27 57 ´ 22 ≈2 46. 63 ´ 37 18 ´ 32 =4 47. 87 ´ 23 26 ´14 =6 48. 92 ´ 41 23 ´ 61 =3 49. (21) 3 = 8000 50. (29) 3 = 27000 51. (18) 4 = 160000 52. (32) 4 = 810000 Making Estimates Continued Fill the gaps Item Quantity Apples Unit cost ($) 1.83 Chickens 8.95 9 Calculator 16.85 7 DVD 9.95 10 4 Estimated cost ($) Fill the gaps Item Quantity Apples Unit cost ($) 1.83 4 Estimated cost ($) 8 Chickens 8.95 9 81 Calculator 16.85 7 140 DVD 9.95 10 100 Fill the gaps Item Quantity Hairdryer Unit cost ($) 23.15 Toaster 47.95 27 Shorts 14.85 74 Chairs 83.75 65 38 Estimated cost ($) Fill the gaps Item Quantity Hairdryer Unit cost ($) 23.15 38 Estimated cost ($) 800 Toaster 47.95 27 1500 Shorts 14.85 74 700 Chairs 83.75 65 5600 Fill the gaps Item Total cost Quantity Shorts 64.91 7 Books 47.99 8 Heaters 3385 9 Fridges 6725 7 Estimated unit cost Fill the gaps Item Total cost Quantity Shorts 64.91 7 Estimated unit cost 9 Books 47.99 8 6 Heaters 3385 9 400 Fridges 6725 7 1000 Fill the gaps Item Total cost Quantity Watches 2225 51 Shoes 4309 78 Calculator 2683 92 Trousers 3416 83 Estimated unit cost Fill the gaps Item Total cost Quantity Watches 2225 51 Estimated unit cost 40 Shoes 4309 78 50 Calculator 2683 92 30 Trousers 3416 83 40 Exercise 12 1. 3 8 =2 2. 3 27 =3 3. 3 1000 = 10 4. 3 1000000 = 100 5. 4 16 =2 6. 4 10000 = 10 7. 5 32 =2 8. 6 64 =2 9. 3 64 =4 10. 64 =8 13. ( ) 7 5 2 =7 10 14. ( ) 6 3 4 =3 24 15. ( ) 2 4 5 =2 20 16. ( ) 3 5 6 =5 18 17. 3 15 7 =7 5 18. 12 3 =3 6 19. 5 30 2 =2 6 20. 4 8 5 =5 2 21. 2 ´2 6 3 =2 9 22. 2 ¸2 6 3 =2 3 23. ( ) 2 6 3 =2 18 24. 3 6 2 =2 2 25. 3 ´3 12 4 =3 16 26. 3 ¸3 12 4 =3 8 27. =3 8