Whole Number Arithmetic
Rounding and estimating
Round to the nearest whole
number
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•
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621.8
19.02
57.04
98.63
1.03
610.8
519.6
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622
19
57
99
1
611
520
Round to one decimal place
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19.023
57.046
81.774
89.522
1.03
2.59
49.97
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19.0
57.0
81.8
89.5
1.0
2.6
50.0
Round to two decimal places
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1.902
5.704
0.1036
2.974
0.006
3.899
0.003
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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
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•
7.56
2.7
4.6
10.6
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8
3
5
10
How many significant figures?
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9.6
2.5
55.1
1.26
22.4
178.3
8.75
3.24
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•
•
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2
2
3
3
3
4
3
3
How many significant figures?
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•
•
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•
46.81
3.808
4.077
71.08
83.881
778.049
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•
•
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4
4
4
4
5
6
How many significant figures?
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•
400.00
40.0
1.4
1.40
1.400
10.0
1.50
100.00
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•
•
•
•
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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?
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0.061
0.007
0.00061
0.46
0.070
0.0700
0.0074
0.07006
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•
•
•
•
•
•
•
2
1
2
2
2
3
2
4
Exercise 9
Rounding
Round the lengths of N. Z.
Rivers to the nearest 10 Km.
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Waikato
Clutha
Wanganui
Taieri
Rangitiki
Waitaki
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•
•
•
425
322
290
288
241
209
Round the lengths of N. Z.
Rivers to the nearest 10 Km.
•
•
•
•
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•
Waikato
Clutha
Wanganui
Taieri
Rangitiki
Waitaki
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•
425 = 430
322 = 320
290 = 290
288 = 290
241 = 240
209 = 210
Round the heights of N. Z.
Mountains to the nearest 100 m.
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Cook
Tasman
Ruapehu
Taranaki
Ngauruhoe
Tongariro
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3764
3498
2797
2518
2291
1968
Round the heights of N. Z.
Mountains to the nearest 100 m.
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•
Cook
Tasman
Ruapehu
Taranaki
Ngauruhoe
Tongariro
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3764 = 3800
3498 = 3500
2797 = 2800
2518 = 2500
2291 = 2300
1968 = 2000
Round the areas of N. Z. Lakes
to the nearest 1000 ha.
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Taupo
Te Anau
Wakatipu
Wanaka
Manapouri
Hawea
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•
60 606
34 447
29 267
19 166
14 245
11 914
Round the areas of N. Z. Lakes
to the nearest 1000 ha.
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Taupo
Te Anau
Wakatipu
Wanaka
Manapouri
Hawea
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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.
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Northland
Auckland
Waikato
Bay of Plenty
Gisborne
Hawkes' Bay
Taranaki
Manawatu - Wanganui
Wellington
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•
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.
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Northland
Auckland
Waikato
Bay of Plenty
Gisborne
Hawkes' Bay
Taranaki
Manawatu - Wanganui
Wellington
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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.
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Nelson
Tasman
Marlborough
West Coast
Canterbury
Otago
Southland
New Zealand
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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.
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•
Nelson
Tasman
Marlborough
West Coast
Canterbury
Otago
Southland
New Zealand
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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
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a. 90 x 6
b. 90 x 60
c. 900 x 60
d. 900 x 600
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540
5400
54 000
540 000
Oral examples - 2
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a.
b.
c.
d.
80 x 5
80 x 50
800 x 50
800 x 500
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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
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560
5600
56 000
560 000
Written examples
5.
6.
7.
8.
40 x 5
40 x 50
400 x 50
400 x 500
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•
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
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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
≈ 8 000
50.
(29)
3
≈ 27 000
51.
(18)
4
≈ 160 000
52.
(32)
4
≈ 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.
150000000
= 500 sec
300000
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.
958000000 1000000000
365 ´ 24
»
400 ´ 20
» 125000km
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
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