1. Limits of accuracy – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Toolbox Notation Finding a lower bound Finding an upper bound Recognising the effect of bounds on a result CONTENTS Using bounds to solve problems

2. Limits of accuracy – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 To say how accurate a measurement is, give its lower and upper bounds. A line l is recorded as having a length of 36 cm to the nearest centimetre. All lines between 35.5 cm and 36.499999… cm are rounded to 36 cm. 35.5 cm is called the lower bound. 36.4999999 is effectively 36.5 cm so 36.5 cm is called the upper bound. This is written as: 35.5  l < 36.5 Another way of writing it is: l = 35  0.5 cm Toolbox MenuBackForward

3. Limits of accuracy – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 The upper and lower bounds of a measurement can be shown in different ways. A and B are the same, C and D are the same. The signs in the inequalities indicate whether the 8.5 is included or not. 1.Which of these measurements are the same? A7.5 kg ≤ w ˂ 8.5 kg Bw = 8 kg (to the nearest kg) Cw = 8 kg (±0.5) D7.5 kg ≤ w ≤ 8.5 kg 2.Write inequalities which describe the measurement of 100 m recorded a)to the nearest metre b)to the nearest 10 centimetres Notation a)99.5 m ≤ length ˂ 100.5 m b)99.9 m ≤ length ˂ 100.1 m MenuToolboxBackForwardAnswer 1 Answer 2

4. Limits of accuracy – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 The lower bound for the length of the pen is 12.5 cm 12 12.513.5 1314 Martin says his pen is 13 cm long to the nearest cm. Finding a lower bound MenuToolboxBackForwardAnswer 1.What is the lower bound for the length of the pen? © Elaine Lambert

5. Limits of accuracy – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 The upper limit is 26 kg 499.9… g as 26.5 kg would be rounded to 27 kg. 25 25.5 26 26.5 27 Stella is flying to Lagos. She can take unaccompanied baggage up to 26 kg (to the nearest kilogram). 1.What is the actual weight limit for her bag? 2.If the plane carries 200 passengers, what is the upper bound for the weight of baggage that the plane could be carrying? Finding an upper bound The upper bound of the weight for one bag is effectively 26.5 kg. 200 × 26.5 = 5300 kg MenuToolboxBackForwardAnswer 1 Answer 2 © Elaine Lambert

6. Limits of accuracy – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Upper bound is 38.45 m. Lower bound is 38.35 m. 38.3 38.35 38.438.5 38.35 The dimensions of a bowling green are 38.4 m × 38.4 m to 3 significant figures. 1.What are the upper and lower bounds for the dimensions of the green? 2.What are the upper and lower bounds of the perimeter of the bowling green? Recognising the effect of bounds on a result Upper bound of perimeter = 4 × 38.45 = 153.8 m. Lower bound of perimeter = 4 × 38.35 = 153.4 m. MenuToolboxBackForwardAnswer 1 Answer 2 38.4 m

7. Limits of accuracy – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 A cable car pod can safely carry 600 kg (±20). The average person weighs 75 kg (± 25). Take the largest person likely to use the lift to be the upper bound of 75 + 25 = 100 kg. Take the lower bound of the weight the pod can carry as 600 – 20 = 580 kg. 580  100 = 5.8 So the maximum number of passengers should be 5. 1.What is the maximum number of people that the pod should carry? Using bounds to solve problems MenuToolboxBackAnswer © Anne Wanjie

8. Limits of accuracy – Worked Examples Mastering Mathematics © Hodder and Stoughton 2014 Editable Teacher Template MenuToolboxBackForwardAnswer 1More Information 1.Task – fixed 2.Task – appears Answer 1 Answer 2 More Answer 2