Limits of Accuracy (Copy)

Practice Questions — 1.10 Limits of Accuracy

Question 1

A length is measured as 52 m correct to the nearest metre.
(a) State the lower bound.
(b) State the upper bound.

Question 2

A mass is measured as 7.4 kg correct to the nearest 0.1 kg.
(a) State the lower bound.
(b) State the upper bound.

Question 3

The width of a desk is measured as 120 cm correct to the nearest 10 cm.
(a) Give the range of possible values of the width.
(b) Express the lower and upper bounds.

Question 4

A student’s weight is given as 62.5 kg, measured correct to the nearest 0.5 kg.
Find the lower and upper bounds.

Question 5

The perimeter of a square is given as 48 cm, measured correct to the nearest cm.
Find the lower and upper bounds of the side length of the square.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

Question 6

A piece of wood has length 3.6 m and width 2.4 m, both measured correct to the nearest 0.1 m.
(a) Find the lower and upper bounds for the area.
(b) Find the lower and upper bounds for the perimeter.

Question 7

A time interval is measured as 4.8 s correct to the nearest 0.1 s.
(a) Find the range of possible values.
(b) State the lower and upper bounds.

Question 8

A car travels 150 km in 2 hours. Both values are measured correct to the nearest 10 km and nearest 5 minutes respectively.
Find the lower and upper bounds of the average speed in km/h.

Question 9

The radius of a circle is given as 8.5 cm correct to the nearest 0.1 cm.
Find the lower and upper bounds for:
(a) the circumference
(b) the area of the circle. (Use π = 3.142)

Question 10

The dimensions of a rectangular field are given as 50 m by 35 m, each correct to the nearest metre.
(a) Find the lower and upper bounds of the perimeter.
(b) Find the lower and upper bounds of the area.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

Answer key and explanations — 1.10 Limits of Accuracy

1.

Length = 52 m correct to the nearest metre.
• Lower bound = 51.5 m
• Upper bound = 52.5 m
Explanation: Half the unit of accuracy (1 m) is 0.5. Subtract for lower, add for upper.

2.

Mass = 7.4 kg correct to the nearest 0.1 kg.
• Lower bound = 7.35 kg
• Upper bound = 7.45 kg
Explanation: Half of 0.1 = 0.05.

3.

Width = 120 cm correct to the nearest 10 cm.
• Lower bound = 115 cm
• Upper bound = 125 cm
Explanation: Half of 10 cm = 5 cm.

4.

Weight = 62.5 kg correct to the nearest 0.5 kg.
• Lower bound = 62.25 kg
• Upper bound = 62.75 kg
Explanation: Half of 0.5 = 0.25.

5.

Perimeter = 48 cm correct to the nearest cm.
Side length = 48 ÷ 4 = 12 cm.
• Lower bound for perimeter = 47.5 cm → side = 47.5 ÷ 4 = 11.875 cm
• Upper bound for perimeter = 48.5 cm → side = 48.5 ÷ 4 = 12.125 cm
Explanation: Divide perimeter bounds by 4.

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

6.

Length = 3.6 m ± 0.05 → (3.55 to 3.65 m)
Width = 2.4 m ± 0.05 → (2.35 to 2.45 m)

(a) Area:
• Lower bound = 3.55 × 2.35 = 8.3425 m²
• Upper bound = 3.65 × 2.45 = 8.9425 m²

(b) Perimeter = 2(L + W)
• Lower bound = 2(3.55 + 2.35) = 11.8 m
• Upper bound = 2(3.65 + 2.45) = 12.2 m

7.

Time = 4.8 s ± 0.05 s → (4.75 s to 4.85 s)
• Lower bound = 4.75 s
• Upper bound = 4.85 s

8.

Distance = 150 km ± 5 km → (145 to 155 km)
Time = 2 h ± 0.083 h (5 min = 1/12 h ≈ 0.083) → (1.917 h to 2.083 h)

Speed = distance ÷ time
• Lower bound speed = 145 ÷ 2.083 ≈ 69.6 km/h
• Upper bound speed = 155 ÷ 1.917 ≈ 80.9 km/h

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course

9.

Radius = 8.5 cm ± 0.05 → (8.45 cm to 8.55 cm)

(a) Circumference = 2πr
• Lower bound = 2 × 3.142 × 8.45 ≈ 53.1 cm
• Upper bound = 2 × 3.142 × 8.55 ≈ 53.7 cm

(b) Area = πr²
• Lower bound = 3.142 × (8.45)² ≈ 224.4 cm²
• Upper bound = 3.142 × (8.55)² ≈ 229.5 cm²

10.

Dimensions: 50 m ± 0.5 (49.5 to 50.5 m), 35 m ± 0.5 (34.5 to 35.5 m)

(a) Perimeter = 2(L + W)
• Lower bound = 2(49.5 + 34.5) = 168.0 m
• Upper bound = 2(50.5 + 35.5) = 172.0 m

(b) Area = L × W
• Lower bound = 49.5 × 34.5 = 1707.8 m²
• Upper bound = 50.5 × 35.5 = 1795.0 m²

Written and Compiled By Sir Hunain Zia, World Record Holder With 154 Total A Grades, 7 Distinctions and 11 World Records For Educate A Change O Level And IGCSE Mathematics Full Scale Course