1. © T Madas

2. Describing the Accuracy of Measurements
Part 1
© T Madas

3. 111 ≤ L ≤ 113 Minimum Length: Maximum Length: 111 mm 113 mm
The length of a pencil is measured as 112 ± 1 mm.
What is the maximum and the minimum possible length of the pencil according to this information?
Lower
Bound
Minimum Length:
Maximum Length:
111 mm
113 mm
Upper
Bound
111 ≤ L ≤
113
© T Madas

4. 2.8 ≤ T ≤ 3.2 Minimum Thickness: Maximum Thickness: 2.8 mm 3.2 mm
The thickness of a coin is measured as 3 ± 0.2 mm.
What is the maximum and the minimum possible thickness of this coin according to this information?
Lower
Bound
Minimum Thickness:
Maximum Thickness:
2.8 mm
3.2 mm
Upper
Bound
2.8 ≤ T ≤
3.2
© T Madas

5. 2.985 ≤ T ≤ 3.015 Minimum Thickness: Maximum Thickness: 2.985 mm
The thickness of an optical lens is measured as 3 ± mm.
What is the maximum and the minimum possible thickness of this lens according to this information?
Lower
Bound
Minimum Thickness:
Maximum Thickness:
2.985 mm
3.015 mm
Upper
Bound
2.985 ≤ T ≤
3.015
© T Madas

6. Describing the Accuracy of Measurements
Part 2
© T Madas

7. The weight of a chocolate bar and its packaging is 72 grams, correct to the nearest gram.
What is the maximum and the minimum possible weight of this object according to this information?
Lower
Bound
Upper
Bound
grams
Minimum Weight:
Maximum Weight:
71.5 g
72.5 g
71.5 ≤ W
<
72.5
© T Madas

8. The length of a pencil is 11.8 cm correct to 1 decimal place.
What is the maximum and the minimum possible length of the pencil according to this information?
Lower
Bound
Upper
Bound cm
Minimum Length:
Maximum Length:
11.75 cm
11.85 cm
11.75 ≤ L
<
11.85
© T Madas

9. The weight of an empty can is 15.32 g correct to 2 decimal places
What is the maximum and the minimum possible weight of the can according to this information?
Repsi Cola
Lower
Bound
Upper
Bound g
Minimum Weight:
Maximum Weight: g g
15.315 ≤ W
<
15.325
© T Madas

10. The shutter time for a camera in cloudy conditions is 0
The shutter time for a camera in cloudy conditions is seconds, correct to 3 decimal places.
What is the maximum and the minimum possible shutter times according to this information?
Lower
Bound
Upper
Bound
sec
Minimum Weight:
Maximum Weight: s s
0.0165 ≤ t
<
0.0175
© T Madas

11. A specialised AC generator used in medicine is said to provide a constant voltage of volts, correct to 4 decimal places.
What is the maximum and the minimum possible voltage that this instrument provides, according to this information?
ESC
LOAD ON
ON BATT
BYPASS
FAULT
generator
Lower
Bound
Upper
Bound
volts
Minimum voltage:
Maximum voltage: V V ≤ V
<
© T Madas

12. The length of a ladybird is 7 mm correct to the nearest mm
What is the maximum and the minimum possible length of the ladybird according to this information?
Lower
Bound
Upper
Bound 10 mm 5
Minimum Length:
Maximum Length:
6.5 mm
7.5 mm
6.5 ≤ L
<
7.5
© T Madas

13. The weight of a male gorilla is measured as 285 kg, correct to the nearest 5 kg.
What is the maximum and the minimum possible weight of this gorilla according to this information?
Lower
Bound
Upper
Bound Kg
Minimum Weight:
Maximum Weight:
282.5 kg
287.5 kg
282.5 ≤ W
<
287.5
© T Madas

14. The winning time of a 100 metre sprinter is 10
The winning time of a 100 metre sprinter is 10.2 seconds correct to the nearest tenth of a second.
What is the fastest and the slowest possible winning times for this particular sprint?
Lower
Bound
Upper
Bound
sec
Fastest Time:
Slowest Time:
10.15 sec
10.25 sec
10.15 ≤ t
<
10.25
© T Madas

15. The time exposure of a photographic film is measured as 0
The time exposure of a photographic film is measured as seconds, correct to the nearest two thousandths of a second.
What is the fastest and the slowest possible exposure times for this particular photographic film?
Lower
Bound
Upper
Bound
sec
Fastest Time:
Slowest Time:
0.035 sec
0.037 sec
0.035 ≤ t
<
0.037
© T Madas

16. The weight of a bean is measured as 8 grams, correct to the nearest quarter of a gram.
What is the maximum and the minimum possible weights for this bean?
Lower
Bound
Upper
Bound
grams
Maximum Weight:
Minimum Weight:
8.125 g
7.875 g
7.875 ≤ w
<
8.125
© T Madas

17. Describing the Accuracy of Measurements
Part 3
© T Madas

18. 55 000 000 ≤ P ≤ 56 499 999 Minimum Population: Maximum Population:
The population of the U.K. is estimated to be , correct to 2 significant figures.
What is the maximum and minimum possible U.K. populations according to this information?
Lower
Bound
Minimum Population:
Maximum Population:
Upper
Bound ≤ P ≤
© T Madas

19. 5625 ≤ s < 5635 Minimum Speed: Maximum Speed: 5625 5635
The speed of a rocket is measured as to be 5630 km per hour, correct to 3 significant figures.
What is the maximum and minimum possible rocket speeds according to this information?
Lower
Bound
Minimum Speed:
Maximum Speed:
5625
5635
Upper
Bound
5625 ≤ s
<
5635
© T Madas

20. 14.5 ≤ P < 15.5 Minimum Length: Maximum Length: 14.5 cm 15.5 cm
The length of a pens is measured as 15 cm, correct to the nearest whole number.
What is the maximum and minimum possible lengths of this pen according to this information?
Lower
Bound
Minimum Length:
Maximum Length:
14.5 cm
15.5 cm
Upper
Bound
14.5 ≤ P
<
15.5
© T Madas

21. Example
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22. Min Perimeter Max Perimeter Min Area Max Area 31.5 + 31.5 + 44.5
A rectangle measures 45 cm by 32 cm.
These dimensions are correct to the nearest cm.
Calculate the minimum possible perimeter of this rectangle
Calculate the maximum possible perimeter of this rectangle
Calculate the minimum possible area of this rectangle
Calculate the maximum possible area of this rectangle
Min Perimeter
– 32.5
31.5
+ 31.5
+ 44.5
+ 44.5
= 152 cm
31.5
Max Perimeter
44.5
– 45.5
32.5
+ 32.5
+ 45.5
+ 45.5
= 156 cm
Min Area
31.5
x 44.5
= cm2
Max Area
32.5
x 45.5
= cm2
© T Madas

23. Example
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24. x Minimum Length Maximum Length
A right angled triangle has perpendicular sides equal to 140 mm and 84 mm.
These dimensions are correct to 2 significant figures.
Calculate the minimum and maximum possible lengths for the hypotenuse, correct to 1 d.p.
Minimum Length
x 2 =
(83.5)2
+ (135)2 c
x 2 = c
x 2 = c
– 145 x
x =
158.7 mm
135
Maximum Length
x 2 =
(84.5)2
+ (145)2 c
x 2 = c
83.5
– 84.5
x 2 = c
x =
167.8 mm
© T Madas

25. Example
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26. The formula is used to calculate the tension T exerted by an elastic spring.
The following data is given, correct to 3 significant figures:
The natural length of the spring L, is m
The extension of the spring x, is m
The modulus of elasticity λ, 1.52 N
Find the maximum and the minimum possible values for the tension exerted by this spring, to 3 significant figures.
0.3855
0.1555
1.515
≤ L ≤
≤ x ≤
≤ λ ≤
0.3865
0.1565
1.525
To maximise T
1.525 x
T =
= 0.619
0.3855
© T Madas

27. To maximise T To minimise T
The formula is used to calculate the tension T exerted by an elastic spring.
The following data is given, correct to 3 significant figures:
The natural length of the spring L, is m
The extension of the spring x, is m
The modulus of elasticity λ, 1.52 N
Find the maximum and the minimum possible values for the tension exerted by this spring, to 3 significant figures.
0.3855
0.1555
1.515
≤ L ≤
≤ x ≤
≤ λ ≤
0.3865
0.1565
1.525
To maximise T
1.525 x
T =
= 0.619
0.3855
To minimise T
1.515 x
T =
= 0.610
0.3865
© T Madas

28. Approximation & bounds
Quick Practice on
Approximation & bounds
© T Madas

29. Write the lower & upper bounds for these measurements
Accuracy
Lower Bound
Upper Bound
175 m
nearest m
174.5 m
175.5 m
45 g
nearest whole number
44.5 g
45.5 g
18 mm
to the nearest mm
17.5 mm
18.5 mm
290 kg
nearest ten
285 kg
295 kg
3300 s
nearest one hundred
3250 s
3350 s
2.3 g
to 1 d.p.
2.25 g
2.35 g
4.08 m
to 2 d.p.
4.075 m
4.085 m
1.234 s
to 3 d.p. s s
10.0 kg
to 1 d.p.
9.95 kg
10.05 kg
0.003 g
to 3 d.p. g g
© T Madas

30. Write the lower & upper bounds for these measurements
Accuracy
Lower Bound
Upper Bound
34 cm
nearest cm
33.5 cm
34.5 cm
56 mm
nearest whole number
55.5 mm
56.5 mm
76 m
to the nearest metre
75.5 m
76.5 m
220 kg
nearest ten
215 kg
225 kg
7800 km
nearest one hundred
7750 km
7850 km
10.8 s
to 1 d.p.
10.75 s
10.85 s
1.77 kg
to 2 d.p.
1.765 kg
1.775 kg
0.456 s
to 3 d.p. s s
305 oz
to the nearest 5 oz
302.5 oz
307.5 oz
602 m
to the nearest 2 metres
601 m
603 m
© T Madas

31. Write the lower & upper bounds for these measurements
Accuracy
Lower Bound
Upper Bound
26 cm
to 2 s.f.
25.5 cm
26.5 cm
870 mm
to 2 s.f.
865 mm
875 mm
315 m
to the nearest five metres
312.5 m
317.5 m
220 kg
nearest ten
215 kg
225 kg
1380 km
to 3 s.f.
1375 km
1385 km
7.6 s
to 1 d.p.
7.55 s
7.65 s
1.17 kg
to 3 s.f.
1.165 kg
1.175 kg
0.024 s
to 2 s.f. s s
12.5 oz
to the nearest ½ oz
12.25 oz
12.75 oz
1.25 m
to the nearest ¼ metre
1.125 m
1.375 m
© T Madas

32. Approximation & bounds
Quick Test on
Approximation & bounds
© T Madas

33. Write the lower & upper bounds for these measurements
Accuracy
Lower Bound
Upper Bound
175 m
nearest m
174.5 m
175.5 m
45 g
nearest whole number
44.5 g
45.5 g
18 mm
to the nearest mm
17.5 mm
18.5 mm
290 kg
nearest ten
285 kg
295 kg
3300 s
nearest one hundred
3250 s
3350 s
2.3 g
to 1 d.p.
2.25 g
2.35 g
4.08 m
to 2 d.p.
4.075 m
4.085 m
1.234 s
to 3 d.p. s s
10.0 kg
to 1 d.p.
9.95 kg
10.05 kg
0.003 g
to 3 d.p. g g
© T Madas

34. Write the lower & upper bounds for these measurements
Accuracy
Lower Bound
Upper Bound
34 cm
nearest cm
33.5 cm
34.5 cm
56 mm
nearest whole number
55.5 mm
56.5 mm
76 m
to the nearest metre
75.5 m
76.5 m
220 kg
nearest ten
215 kg
225 kg
7800 km
nearest one hundred
7750 km
7850 km
10.8 s
to 1 d.p.
10.75 s
10.85 s
1.77 kg
to 2 d.p.
1.765 kg
1.775 kg
0.456 s
to 3 d.p. s s
305 oz
to the nearest 5 oz
302.5 oz
307.5 oz
602 m
to the nearest 2 metres
601 m
603 m
© T Madas

35. Write the lower & upper bounds for these measurements
Accuracy
Lower Bound
Upper Bound
26 cm
to 2 s.f.
25.5 cm
26.5 cm
870 mm
to 2 s.f.
865 mm
875 mm
315 m
to the nearest five metres
312.5 m
317.5 m
220 kg
nearest ten
215 kg
225 kg
1380 km
to 3 s.f.
1375 km
1385 km
7.6 s
to 1 d.p.
7.55 s
7.65 s
1.17 kg
to 3 s.f.
1.165 kg
1.175 kg
0.024 s
to 2 s.f. s s
12.5 oz
to the nearest ½ oz
12.25 oz
12.75 oz
1.25 m
to the nearest ¼ metre
1.125 m
1.375 m
© T Madas

36. © T Madas