Whole Number Arithmetic

Rounding and estimating

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)

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

How many significant figures?

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 Population Min. Pop Max. Pop

North Shore 172 000 171 500 172 499

Waitakere 156 000

Auckland 346 000

Manukau 254 000

This table shows the population of Auckland's 4 cities rounded to the nearest 1000.

Copy down and complete the table.

City Population Min. Pop Max. Pop

North Shore 172 000 171 500 172 499

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. 80 x 5 • b. 80 x 50 • c. 800 x 50 • d. 800 x 500

• 400• 4000• 40 000• 400 000

Oral examples - 3

= 50

Oral examples - 3

= 50

Oral examples - 3

= 500

Oral examples - 3

= 500

Oral examples - 4

= 200

Oral examples - 4

= 200

Oral examples - 4

= 2000

Oral examples - 4

= 2000

Written examples

1. 80 x 7

2. 80 x 70

3. 800 x 70

4. 800 x700

• 560• 5600• 56 000• 560 000

Written examples

5. 40 x 5

6. 40 x 50

7. 400 x 50

8. 400 x 500

• 200• 2000• 20 000• 200 000

9.

= 50

10.

= 50

11.

= 500

12.

= 500

13.

= 200

14.

= 20

15.

= 2000

16.

= 2000

Estimation

Answers are not exact

Exercise 10

17. 91 x 18 18. 82 x 2919. 73 x 36 20. 64 x 4721. 621 x 1922. 685 x 3223. 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.

≈ 5

26.

≈ 2

27.

≈ 4

28.

≈ 3

29.

≈ 40

30.

≈ 30

31.

≈ 20

32.

≈ 50

33.

≈ 400

34.

≈ 2500

35.

≈ 90 000

36.

≈ 160 000

37.

≈ 10

38.

≈ 20

39.

≈ 30

40.

≈ 100

41.

≈ 40

42.

≈ 20

43.

≈ 60

44.

≈ 30

45.

≈ 2

46.

≈ 4

47.

≈ 6

48.

≈ 3

49.

≈ 8 000

50.

≈ 27 000

51.

≈ 160 000

52.

≈ 810 000

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.

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.

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.

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.

55.

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

55.

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

• 110000 km

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.)

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

Making Estimates

Continued

Fill the gaps

Item Unit cost ($)

Quantity Estimated cost ($)

Apples 1.83 4

Chickens 8.95 9

Calculator 16.85 7

DVD 9.95 10

Fill the gaps

Item Unit cost ($)

Quantity Estimated cost ($)

Apples 1.83 4 8

Chickens 8.95 9 81

Calculator 16.85 7 140

DVD 9.95 10 100

Fill the gaps

Item Unit cost ($)

Quantity Estimated cost ($)

Hairdryer 23.15 38

Toaster 47.95 27

Shorts 14.85 74

Chairs 83.75 65

Fill the gaps

Item Unit cost ($)

Quantity Estimated cost ($)

Hairdryer 23.15 38 800

Toaster 47.95 27 1500

Shorts 14.85 74 700

Chairs 83.75 65 5600

Fill the gaps

Item Total cost Quantity Estimated unit cost

Shorts 64.91 7

Books 47.99 8

Heaters 3385 9

Fridges 6725 7

Fill the gaps

Item Total cost Quantity Estimated unit cost

Shorts 64.91 7 9

Books 47.99 8 6

Heaters 3385 9 400

Fridges 6725 7 1000

Fill the gaps

Item Total cost Quantity Estimated unit cost

Watches 2225 51

Shoes 4309 78

Calculator 2683 92

Trousers 3416 83

Fill the gaps

Item Total cost Quantity Estimated unit cost

Watches 2225 51 40

Shoes 4309 78 50

Calculator 2683 92 30

Trousers 3416 83 40