AQA GCSE Maths Foundation Student Workbook

6

Number: Approximations

This chapter is going to show you: ●

how to round a number to a given accuracy

●

how to estimate the answer to calculations by rounding

●

how to find the limits of numbers rounded to a given accuracy

●

how to work out the error interval due to rounding or truncation.

You should already know: ●

how to multiply and divide whole numbers.

About this chapter You have probably heard people ask for a ‘ball park’ figure. It comes from newspapers in the US reporting on crowds at baseball games. They generally give the numbers to the nearest thousand, for example: ‘40 000 fans watch the Red Sox beat the Yankees.’ The number 40 000 is an approximate value, but close enough to give a good idea of the number of people in the ‘ball park’.

If you think about it, you will probably realise that you talk in approximate numbers every day. For example, you may say that it takes you about 20 minutes to get to school or that your mobile phone costs about £30 a month, or a car journey will take about two and a half hours.

It is important that you can round numbers accurately. You also need to have an idea of what it actually means when numbers are given approximately. For example, when a hotel claims to be ‘approximately 5 minutes’ walk from the beach!’ it is probably going to take you a bit longer than that!

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6.1 Rounding whole numbers This section will show you how to:

Key term

Apple pie

round a whole number.

●

round

The D

aily

Pl 23 000 people ran the marath on I drive for 40 minutes to get to school.

On a packet of mints you may see the contents given as, for example: ‘Average contents: 30 mints’. If you know that this number is rounded to the nearest 10, then: the smallest number that is rounded up to 30 is 25

●

the largest number that is rounded down to 30 is 34 (because 35 would be rounded up to 40).

●

So, there could actually be from 25 to 34 mints in the packet.

What about the number of runners in a marathon? If you know that the number 23 000 is rounded to the nearest 1000: the smallest number that is rounded up to 23 000 is 22 500

●

the largest number that is rounded down to 23 000 is 23 499 (because 23 500 would be rounded up to 24 000).

●

So, there could actually be from 22 500 to 23 499 people in the marathon.

Do you think the cooking time on a pie is a rounded value? Does a cooking time of 30 minutes mean that you could cook it for any time between 25 and 35 minutes? This is different because it is generally unsafe to undercook food. Most cooks would bake the pie for at least 30 minutes. If it is cooked for too long it will burn, so 35 minutes is probably the maximum time.

Do you think the time it takes the teacher to drive to school is rounded? Does the journey always take between 35 and 45 minutes? Traffic conditions vary a lot, so 40 minutes is probably an average.

Most numbers used on a daily basis are estimates, sensible values or averages.

6.1 Rounding whole numbers

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Example 1

a Round these numbers to the nearest 10.

i

53

ii

67

b Round these numbers to the nearest 100.

i

489

ii

821

a

i

50

ii

70

b

i 500

ii

800

iii

iii

125

iii 1350

130

iii 1400

Note that the rule for a ‘halfway’ value is to round up.

Exercise 6A 1

2

3

Round each number to the nearest 10.

a 24

b 57

c 78

d 54

e 96

f 21

g 88

h 66

i

j

k 29

l

m 77

n 49

o 94

51

14

26

Round each number to the nearest 100.

a 240

b 570

c 780

d 504

e 967

f 112

g 645

h 358

i

j

k 350

l

m 750

n 1020

650

998

1050

o 1070

These three jars are on the shelf of a sweet shop.

Jar 1

Jar 2

80

Jar 3

120

sweets (to the nearest 10)

190

sweets (to the nearest 10)

sweets (to the nearest 10)

Look at each number below and write down which jar it could be describing. (For example, could there be 76 sweets in jar 1?)

4

140

a 78 sweets

b 119 sweets

c 84 sweets

d 75 sweets

e 186 sweets

f 122 sweets

g 194 sweets

h 115 sweets

i

j

k 192 sweets

l

81 sweets

79 sweets

124 sweets

m Which of these numbers of sweets could not be in jar 1?

74 84 81 76

n Which of these numbers of sweets could not be in jar 2?

124 126 120 115

o Which of these numbers of sweets could not be in jar 3?

194 184 191 189

Round each number to the nearest 1000.

a 2400

b 5700

c 7806

d 5040

e 9670

f 1120

g 6450

h 3499

i

j

k 2990

l

5110

m 7777

n 5020

o 9400

p 3500

q 6500

r 7500

s 1020

t 1770

9098

1500

6 Number: Approximations

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5

MR

6

Round each number to the nearest 10.

a 234

b 567

c 718

d 524

e 906

f 231

g 878

h 626

i

j

k 375

l

m 345

n 1012

625

114

296

o 1074

Look at these signs.

Welcome to Elsecar

Welcome to Hoyland

Welcome to Jump

Population 800 (to the nearest 100)

Population 1200 (to the nearest 100)

Population 600 (to the nearest 100)

Which of these sentences could be true? Which must be false?

a There are 789 people living in Elsecar. b There are 1278 people living in Hoyland. c There are 550 people living in Jump. d There are 843 people living in Elsecar. e There are 1205 people living in Hoyland. f There are 650 people living in Jump.

MR

7

The sign-maker who made the signs in question 6 is making a similar sign for Drayton. Drayton has a population of 1385.

Draw a diagram to show what she should write on the sign.

8

The table shows the numbers of spectators in the crowds at ten Premier Division games on a weekend in October 2014.

Match

Number of spectators

Burnley v Everton

19 927

Liverpool v Hull City

44 591

Man Utd v Chelsea

75 327

QPR v Aston Villa

18 022

Southampton v Stoke

30 017

Sunderland v Arsenal

44 449

Swansea v Leicester

20 259

Tottenham v Newcastle

35 650

West Brom v Crystal Palace

24 738

West Ham v Man City

34 977

a Which match had the largest crowd? b Which had the smallest crowd? c Round all the numbers to the nearest 1000. d Round all the numbers to the nearest 100.

6.1 Rounding whole numbers

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9

PS

10

Give these times to the nearest 5 minutes.

a 34 minutes

b 57 minutes

c 14 minutes

d 51 minutes

e 8 minutes

f 13 minutes

g 44 minutes

h 32.5 minutes

i

j

3 minutes

50 seconds

Matthew and Vikki are playing a game with whole numbers.

a Matthew is thinking of a number. Rounded to the nearest 10, it is 380.

What is the smallest number Matthew could be thinking of?

b Vikki is thinking of a different number. Rounded to the nearest 100, it is 400. If Vikki’s number is definitely smaller than Matthew’s, what are the smallest and largest possible numbers that Vikki is thinking of?

PS

11

The number of adults attending a comedy show is 80, to the nearest 10.

The number of children attending is 50, to the nearest 10.

Katie says that 130 adults and children attended the comedy show.

Give an example to show that she may not be correct.

6.2 Rounding decimals

Key terms

This section will show you how to:

decimal fraction

●

decimal place

round decimal numbers to a given accuracy.

The decimal number system carries on after the decimal point to include decimal fractions, with place values for tenths, hundredths, thousandths and so on.

decimal point error interval

The decimal point separates the decimal fraction from the whole-number part of the number.

For example, the number 25.374 is made up of: Tens

Units

tenths

10

1

2

5

.

hundredths

thousandths

1 10

1 100

1000

3

7

4

1

You use decimal notation to express amounts of money. For example: £32.67

means 3 × £10 2 × £1 6 × £0.10

(10 pence)

7 × £0.01

(1 penny)

When you write a number in decimal form, the positions of the digits to the right of the decimal point are called decimal places (dp). For example: ●

79.4 is written ‘with one decimal place’

●

6.83 is written ‘with two decimal places’

●

0.526 is written ‘with three decimal places’.

When a rounded number is written with a zero, for example, 3.50 (2 dp), it means that the number, before rounding, was possibly 3.495 of 4.99. The zero shows that the rounded number is accurate to two decimal places.

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These are the steps to round a decimal number to a given number of decimal places. ●

●

If the value of this digit is less than 5, just remove this and the digits after it.

If the value of this digit is 5 or more, add 1 to round up the digit in the previous decimal place and then remove any digits after the one you have rounded.

Example 2

●

Count along the decimal places from the decimal point and look at the digit after the one to be rounded.

Round these numbers. a 5.852 to 2 dp

b 7.156 to 2 dp

c

d 15.3518 to 1 dp

0.274 to 1 dp

a 5.852 rounds to 5.85 to 2 dp.

b 7.156 rounds to 7.16 to 2 dp.

c 0.274 rounds to 0.3 to 1 dp.

d 15.3518 rounds to 15.4 to 1 dp.

When a number has been rounded, you need to know what the original number may have been.

For example, when a number is given as ‘4.5 to one decimal place’, then it could originally have been somewhere between 4.45 and 4.55. It could not have been exactly 4.55 as this would be round up to 4.6.

You can use inequalities to show this. You write: 4.45  actual value < 4.55 This is the error interval due to rounding. It means that the original number could be from 4.45 to 4.55 but not 4.55.

Hints and tips The sign  means that the value 4.45 is included; the sign < means that the value

Example 3

4.55 is not included.

a A number is stated as 6, measured to the nearest whole number. Use inequalities to write down the error interval due to rounding. b A piece of wood is 2.4 metres long. This length is given correct to one decimal place. Brad needs a piece 2.38 metres long. Use the error interval to show that Brad cannot be sure that this piece of wood is long enough. a The value could be as low as 5.5 and as high as 6.5, but not actually 6.5, so the error interval is 5.5  value  6.5. b The error interval is 2.35  length  2.45, so it could be shorter than 2.38 metres.

Exercise 6B 1

Round each number to one decimal place.

a 4.83

b 3.79

c 2.16

d 8.25

e 3.673

f 46.935

g 23.883

h 9.549

i

j

k 64.99

l

0.109

0.599

50.999

Hints and tips Just look at the value of the digit in the second decimal place.

2

Round each number to two decimal places.

a 5.783

b 2.358

c 0.977

d 33.085

e 23.5652

f 91.7895

g 7.995

h 2.3076

i

j

k 96.508

l

5.9999

3.5137

0.009 6.2 Rounding decimals

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3

4

Round each number to the number of decimal places (dp) indicated.

a 4.568 (1 dp)

b 0.0832 (2 dp)

c 45.71593 (3 dp)

d 94.8531 (2 dp)

e 602.099 (1 dp)

f 671.7629 (2 dp)

g 7.1124 (1 dp)

h 6.90354 (3 dp)

i 13.7809 (2 dp)

j 0.07511 (1 dp)

k 4.00184 (3 dp)

l 59.983 (1 dp)

Round each number to the nearest whole number.

a 8.7 e 7.82 i 1.514 MR

5

b 9.2 f 7.55 j 46.78

c 6.5 g 6.172 k 153.9

d 3.28 h 3.961 l 342.5

Belinda puts these items in her shopping basket: bread (£1.09), meat (£6.99), cheese (£3.91) and butter (£1.13).

By rounding each price to the nearest pound (£), work out an estimate for the total cost of the items.

MR

6

Which of these numbers are correctly rounded values of 3.456?

3

PS

7

3.0

3.4

3.40

3.45

3.46

3.47

3.5

3.50

When an answer is rounded to three decimal places, it is 4.728.

Which of these could be the original answer?

4.71

PS

4.7275

4.7282

4.73

8

A number has three decimal places. When it is rounded to two decimal places it is 6.45. When it is rounded to one decimal place, it is 6.4. Work out a possible value of the number.

9

A number is given as 8.8 correct to one decimal place. Write down the error interval due to rounding.

PS

10

Jake had £8 in change, to the nearest pound. To the nearest 10p he had £8.50 in change. How much change could he have had?

PS

11

A rectangle is 6.5 cm long and 3.3 cm wide. Both of these values are given correct to one decimal place.

a Write down the error interval due to rounding of the length. b Use error intervals of the length and width to show that the perimeter has an error interval of 19.4  perimeter  19.8.

c Use error intervals for the length and width to write down the smallest possible value for the area.

MR

12

π is a never-ending decimal. A commonly used under-estimate is 3.14. A commonly used over-estimate is 3.142. The formula for the circumference, C, of a circle with diameter, d, is C = πd. The diameter of a circle is measured as 10 cm, to the nearest centimetre. Work out:

a the smallest possible under-estimate of the circumference b the greatest possible over-estimate of the circumference.

PS

13

A number is given correct to 3 decimal places. It is rounded to 2 decimal places. This answer is then rounded to 1 decimal place, to give the value 3.7.

Work out the smallest possible value that the original number could have had.

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6 Number: Approximations

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6.3 Approximating calculations This section will show you how to:

Key terms

●

identify significant figures

●

round numbers to a given number of significant figures

●

use approximation to estimate answers and check calculations

●

round a calculation at the end of a problem, to give what is considered to be a sensible answer.

approximate significant figure

Rounding to significant figures You often use significant figures (sf) when you want to approximate a number that has lots of digits in it.

This table shows some numbers written to one, two and three significant figures.

One sf

8

Two sf

67

4.8

Three sf

312

65.9

50

200

90 000

0.76 40.3

0.000 07

45 000

730

0.0761

7.05

0.003

0.4

0.0067

0.40

0.003 01

0.400

These are the steps for rounding a number to one significant figure. They are very similar to those used for rounding to one decimal place. ●

From the left, find the first non-zero digit. The next digit is the second digit.

●

When the value of the second digit is less than 5, leave the first (non-zero) digit as it is.

●

When the value of the second digit is equal to or greater than 5, add 1 to the first (non-zero) digit.

●

●

If the original number is greater than 1, replace all other digits after the rounded digit, as far as the decimal point, with zeros. If there were some decimal values do not include them.

If the original number is less than 1 (it starts 0), write down all the zeros before the rounded digit and delete everything after the rounded digit.

To round to two significant figures, you use the same method but use the third (non-zero) digit from the left.

This table shows some numbers rounded to one or two significant figures.

Number

Rounded to

Number

Rounded to

1 sf

2 sf

78

80

78

45 281

50 000

45 000

32

30

32

568

600

570

8054

8000

0.692

0.7

0.69

1.894

2

1.9

998

1000

0.436

1 sf

7.867

1000

0.4

99.8

0.44

0.0785

2 sf

8100

8 100

7.9 100

0.08

0.079

Exercise 6C 1

Round each number to one significant figure.

a 46 313

b 57 123

c 30 569

d 94 558

e 85 299

f 54.26

g 85.18

h 27.09

i

j

k 0.5388

l

m 0.00584

n 0.04785

o 0.000876

p 9.9

q 89.5

r 90.78

s 199

t 999.99

0.2823

96.432

167.77

6.3 Approximating calculations

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2

3

4

Round each number to two significant figures.

a 56 147

b 26 813

c 79 611

d 30 578

e 14 009

f 5876

g 1065

h 847

i

j

k 1.689

l

m 2.658

n 8.0089

o 41.564

p 0.8006

q 0.458

r 0.0658

s 0.9996

t 0.00982

a 64 523

b 19 316

c 4.5489

d 4.0756

e 14.396

f 6.689

g 1.072

h 9428

i

j

6

10.37

9.6821

Write down the smallest and the greatest numbers of sweets that can be found in each of these jars, when full.

70

MR

638.7

Round each number to three significant figures.

100

sweets (to 1sf)

5

4.0854

109

sweets (to 1sf)

1000 sweets (to 1sf)

Write down the smallest and the greatest numbers of people that live in these towns.

Ayton

population 800 (to 1 sf)

Beeville

population 1000 (to 1 sf)

Charlestown

population 200 000 (to 1 sf)

When a number with one decimal place is rounded to 2 sf it is 64 and rounded to 1 sf it is 60.

a What is the largest possible value of the number? b What is the smallest possible value of the number?

MR

7

A joiner estimates that he has 20 pieces of skirting board in stock. This is correct to one significant figure. He uses three pieces and now has 10 left, still correct to one significant figure.

How many pieces could he have had to start with? Work out all possible answers.

PS

8

There are 500 fish in a pond, correct to one significant figure.

What is the smallest possible number of fish that could be taken from the pond so that there are 400 fish in the pond, correct to one significant figure?

PS

9

The organisers of a conference expect 2000 people (to 2 sf) to attend. The venue can seat 1850 (to 3 sf). In the event, 100 people had to stand. How many people attended the conference? Write down a range of values.

Approximating calculations How do you approximate the value of a calculation?

What would you actually do when you try to approximate an answer to a problem?

For example, what is the approximate answer to 35.1 × 6.58?

To find the approximate answer, round each number to one significant figure, then complete the calculation. So, in this case, the approximation is: 35.1 × 6.58 ≈ 40 × 7 = 280

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Hints and tips The symbol ≈ means ‘approximately equal to’.

Example 4

The approximation for the division 89.1 ÷ 2.98, is 90 ÷ 3 = 30.

Find an approximate answer to 24.3 ÷ 3.87.

Round each number in the calculation to 1 sf. 24.3 ÷ 3.87 ≈ 20 ÷ 4 = 5 So 24.3 ÷ 3.87 ≈ 5.

A quick approximation will help prevent you from giving an answer that is much too big or too small.

Exercise 6D 1

Work out approximate answers to these calculations.

a 5435 × 7.31

b 5280 × 3.211

c 63.24 × 3.514 × 4.2

d 3508 × 2.79

e 72.1 × 3.225 × 5.23

f 470 × 7.85 × 0.99

g 354 ÷ 79.8

h 36.8 ÷ 1.876

i 5974 ÷ 5.29

Use a calculator to see how close your approximations are to the actual answers.

2

3

Work out the approximate monthly pay for each annual salary given.

a £35 200

b £25 600

c £18 125

d £8420

Work out each person’s approximate annual pay.

a Kevin who earns £270 a week b Malcolm who earns £1528 a month c David who earns £347 a week MR

4

A farmer bought 2713 kg of seed at a cost of £7.34 per kilogram. Estimate the total cost of this seed.

5

By rounding, work out an approximate answer to each calculation.

6

a

573 + 783 107

b

783 − 572 24

c

352 + 657 999

d

1123 − 689 354

e

589 + 773 658 − 351

f

793 − 569 998 − 667

g

354 + 656 997 − 656

h

1124 − 661 355 + 570

i

28.3 × 19.5 97.4

j

78.3 × 22.6 3.69

k

3.52 × 7.95 15.9

l

11.78 × 77.8 39.4

Work out an approximate answer for each calculation.

a 208 ÷ 0.378

b 96 ÷ 0.48

c 53.9 ÷ 0.58

d 14.74 ÷ 0.285

e 28.7 ÷ 0.621

f 406.9 ÷ 0.783

Use a calculator to see how close your approximations are to the actual answers.

7

A litre of paint will cover an area of about 8.7 square metres (m2). Approximately how many 1-litre cans will I need to paint a room with a total surface area of 73 m2?

6.3 Approximating calculations

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8

By rounding, work out an approximate answer to each calculation.

a CM

9

84.7 + 12.6 0.483

b

32.8 × 71.4 0.812

c

34.9 − 27.9 0.691

d

12.7 × 38.9 0.42

It took me 6 hours and 40 minutes to drive from Sheffield to Bude, a distance of 295 miles. My car uses petrol at the rate of about 32 miles per gallon. The petrol cost £3.51 per gallon.

a Approximately how many miles did I travel each hour? b Approximately how many gallons of petrol did I use in driving from Sheffield to Bude?

c What was the approximate cost of all the petrol for my journey from Sheffield to Bude and back again?

PS

10

Kirsty puts magazines inside envelopes and sticks an address label on each one. She puts 178 magazines in envelopes and addresses them between 10:00 am and 1:00 pm.

Approximately how many magazines will she be able to deal with in a week in which she works for 17 hours?

EV

11

An athlete runs 3.75 km every day. A marathon is 42.1 kilometres. The athlete claims the distance he ran was the equivalent of over three marathons a month. Is this claim true?

MR

12

1 kg = 1000 g A box full of magazines weighs 8 kg. One magazine weighs about 15 g. Approximately how many magazines are there in the box?

13

An apple weighs about 280 g.

a What is the approximate mass of a bag containing a dozen apples? b Approximately how many apples will there be in a sack weighing 50 kg?

14

At the 2015 American Football final between the New England Patriots and the Seattle Seahawks, in Arizona, the average price of a ticket was $2670. The attendance at the game was 70 288.

A Estimate how much money was made from ticket sales.

B Each team gets 17.5% of the money made from ticket sales. Estimate how much each team made.

MR

15

The error interval of the answer, A, to the calculation N × 15 is: 112.5  A < 127.5 Work out the error interval of N. Give your answer in the form X  N < Y, where X and Y are decimal numbers.

16

The lengths in this rectangle are measured to the nearest centimetre.

a Work out the error interval of the length.

10 cm

b Work out the error interval of the width. c Work out the error interval of the perimeter

5 cm

d Work out the error interval of the area.

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Worked exemplars PS

1 The perimeter of a square is 36 cm.

This length is accurate to the nearest centimetre.

Work out the error interval due to rounding of the length of a side of the square.

This is a problem-solving question, so you need to make connections between different topics in mathematics (in this case properties of squares and rounding) and to show your strategy clearly.

Perimeter = 4 × length of one side

Write down the correct formula for the perimeter of a square.

Error interval of perimeter is:

Write down the error interval of the perimeter.

35.5  perimeter  36.5

Show that the error interval of a side is a Error interval of one side is 41 of the quarter of the error interval of the perimeter. error interval of the perimeter.

Error interval of one side is:

Write down the error interval of the side.

8.875  length of side  9.125 MR

2 Use estimation to put the expressions below in order of size, starting with the smallest.

A

9.7 × 10.3 B 7.2 − 2.1

88.8 ÷ 5.8

C

(

)

3.7 + 6.2 2 1.9

This is a mathematical reasoning question. You need to show your working and your conclusion.

A:

10 × 10 100 = 7–2 5

Round all the numbers in each expression to 1 sf and work out the approximate value.

= 20

B: 90 ÷ 6 = 15 C:

( ) ( )

4+6 2 10 2 = 2 2

= 52 = 25

The order from smallest is:

Write down the order, starting with the smallest.

B, A, C MR

3 The length of a piece of wood is measured as 2.3 metres to the nearest 10 cm. Which of these is the error interval for the length?

A 2.2 m  length < 2.3 m

B 1.3 m  length < 3.3 m

C 2.25 m  length < 2.35 m

D 2.29 m  length < 2.31 m

This is a mathematical reasoning question as there is a mixture of units. The length is given in metres but the accuracy is measured in centimetres.

2.3 metres = 230 centimetres

Change the length to centimetres.

Error interval is 225  length < 235

An accuracy of 10 cm means that the length is within ± 5 cm.

2.25 m  length < 2.35 m

Convert the error interval back to metres.

6 Worked exemplars

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Ready to progress?

I can identify the number of decimal places.

I can round numbers to a given number of decimal places.

I can round decimals and whole numbers to a given number of significant figures.

I can use approximations to estimate the answer to calculations.

I can use inequality notation to specify the error interval due to rounding.

Review questions 1

a Write the number 5639 correct to the nearest 1000.

b Write the number seven hundred and eighty-six correct to the nearest 10.

2

a Write the number 3185 correct to the nearest hundred. b Write the number 5472 correct to the nearest thousand.

3

a Write these numbers in figures. i thirty-six million

ii three thousand, six hundred

b What number should go in each box to make these calculations correct? i 36 Ă&#x2014; = 36 000 4

ii 36 000 000 á = 360 000

Ben Nevis is 1344 metres high.

Mount Snowdon is 1085 metres high.

a How much higher is Ben Nevis than Mount Snowdon?

Give your answer to the nearest 10 metres.

b Round the height of each mountain to the nearest 10 metres and then work out the difference between them.

c Are your results for parts a and b the same? Explain why.

CM

5

The population of Plaistow in 2014 is given as 7700 correct to the nearest hundred.

a What is the smallest possible population of Plaistow? b What is the largest possible population of Plaistow?

6

A seal colony is estimated to have 2500 seals, correct to the nearest 100.

a What is the smallest possible number of seals in the colony? b What is the largest possible number of seals in the colony? c Better counting methods now show the colony to be 2500 correct to the nearest 50.

What is i the smallest

150

ii the largest number of seals now?

6 Number: Approximations

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7

How many decimal places are there in each number?

a 6.82 8

9

b 9.705

c 0.009

d 10.0708

How many significant figures are there in each number?

a 58

b 6000

c 0.0092

d 204

e 18.5

f 10.52

g 0.0106

h 300 000

Round these numbers to the accuracy shown.

a 67.493 (1 dp)

b 30.6 (2 sf)

c 2999 (2 sf)

d 3.99 (1 dp)

e 23 (1 sf)

f 12.35 (1 dp)

g 13.567 (2 dp)

h 29.3764 (3 sf)

PS

10

A bus has 52 seats. 10 people are allowed to stand.

The bus has 40 passengers, counted to the nearest 10. At a bus stop there are 20 people measured to the nearest 10. No one gets off the bus. Can you be sure that everyone at the bus stop will get on the bus? Show how you decide.

PS

11

This is a postcard. The lengths are accurate to the nearest half-centimetre.

12.5 cm

This is an envelope. The lengths are accurate to the nearest centimetre.

8 cm

Will every postcard fit in every envelope? Show how you decide.

9 cm

13 cm

PS

12

A number has three decimal places. When it is rounded to two decimal places it is 1.85. When it is rounded to one decimal place it is 1.9. Work out the range of values for the number.

PS

13

A number is 200 when rounded to the nearest hundred and 240 when rounded to the nearest ten. What are the greatest and least possible values of the number?

MR

14

Machine A makes square holes. Each hole has a side of 50 mm, measured to the nearest millimetre.

Machine B makes round pegs. Each peg has a diameter of 49 mm, measured to the nearest 2 millimetres.

a Use inequalities to write down the error interval for the side of the square. b Will every round peg fit in every square hole? Show your working.

15

The lengths in this right-angled triangle are measured to the nearest centimetre.

a Work out the error interval of the perimeter.

3 cm

5 cm

b Work out the error interval of the area.

4 cm

6 Review questions

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