Cambridge Lower Secondary Maths Workbook 7

Chapter 1

Place value and rounding Place value

Summary of key points Each digit in a whole number or decimal number has a place value.

1 000 000 millions

100 000

10 000

1 000

100

hundred ten thousands hundreds thousands thousands

10

1

.

0.1

tens

ones

decimal point

tenths

0.01

0.001

hundredths thousandths

To multiply a number by 10 (or 100 or 1000), move each digit one (or two or three) places to the left.

To divide a number by 10 (or 100 or 1000), move each digit one (or two or three) places to the right.

Exercise 1 1

Write the value of the digit 2 in each of these whole numbers.

Example:

2

4216

2 hundreds

a) 521

…………………

f) 25 916

…………………

b) 7214

…………………

g) 9 294 007

…………………

c) 1032

…………………

h) 2 640 000

…………………

d) 2969

…………………

i) 4 021 308

…………………

e) 4120

…………………

j) 42 879 301

…………………

Write each decimal in the correct position in the table to show the value of the digit 8. The first decimal has been entered for you to show you what to do.

A

52.186

B

6.84

C

8.07

D

14.08

E

24.258

F

83.694

G

46.825

H

103.148

I

254.085

J

16.8156

K

0.0083

L

18.2033

8 tens

8 units

8 tenths

8 hundredths

8 thousandths

A

Chapter 1: Place value and rounding

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4

Work out: a) 47 × 100

…………………

f) 30.7 × 10

…………………

b) 359 × 1000

…………………

g) 0.164 × 1000

…………………

c) 0.64 × 10

…………………

h) 7.06 × 1000

…………………

d) 201 × 1000

…………………

i) 0.003 5 × 10

…………………

e) 2.65 × 100

…………………

j) 1.375 2 × 100

…………………

…………………

f) 71 ÷ 100

…………………

b) 819 000 ÷ 1000 …………………

g) 5.3 ÷ 100

…………………

c) 64 ÷ 10

…………………

h) 9 ÷ 1000

…………………

d) 3600 ÷ 1000

…………………

i) 0.65 ÷ 10

…………………

e) 8.5 ÷ 10

…………………

j) 0.024 ÷ 100

…………………

Work out: a) 7200 ÷ 100

5

Find the missing number in each of these calculations. a) 64.2 × …….. = 642

g) …….. ÷ 10 = 4.63

b) 0.025 × 1000 = ……..

h) …….. ÷ 1000 = 8.47

c) …….. × 100 = 650

i) Challenge

d) 10 × …….. = 945 e) 56 ÷ 1000 = ……..

45 × 10 = …….. × 1000 j) Challenge 0.062 × …….. = 620 ÷ 1000

f) 341 ÷ …….. = 3.41 6

7

8

A piece of paper is 0.06 mm thick. There are 1000 sheets of paper in a pile. Work out the height of the pile.

Zoe has 10 identical coins. The total mass of all the coins is 138.5 g.

Work out the mass of each coin.

……….mm

……….g

Use the numbers from the box to complete these calculations.

Each number should be used only once.

3.05 0.035

…….. × 1000 = …….. …….. ÷ 10 = ……..

350

3500 3050 3.5

…….. × 100 = …….

2

Unit 1A: Number and calculation

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Orla says, “To multiply a number by 10, add a 0 to the end of it.” a) Give an example to show that Orla’s rule sometimes works. …………………………………………………………………………………………….. b) Give an example to show that Orla’s rule does not always work. ……………………………………………………………………………………………..

Think about 10 Summarise the methods for multiplying and dividing a number by 10, 100 and 1000.

Ordering decimals and measurements

Summary of key points To decide which of two decimals is larger, make sure both have the same number of decimal places. If necessary add zeros to the end of one of them.

Example: Which of 0.37 or 0.326 is larger?

Add a zero to the first decimal so that both have three decimal places.

0.37

0.370

0.326

It is then easier to see that 0.37 is larger.

Changing between common metric units: ÷ 100

centimetres

÷ 1000

÷ 1000

metres

grams

× 100

millilitres

kilograms

litres

× 1000

× 1000

Exercise 2 1

Write the largest number in each pair. a) 0.82 or 0.38

…………………

e) 0.48 or 0.5

…………………

b) 6.05 or 6.5

…………………

f) 0.7 or 0.67

…………………

c) 1.46 or 1.6

…………………

g) 0.4 or 0.945

…………………

d) 0.2 or 0.18

…………………

h) 0.66 or 0.802 …………………

Chapter 1: Place value and rounding

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Write the smallest measurement in each pair. a) 209 cm or 2 m

…………………

e) 4.6 kg or 8700 g …………………

b) 7 kg or 650 g

…………………

f) 40 ml or 0.3 l

c) 3.5 l or 29 ml

…………………

g) 45 cm or 0.09 m …………………

d) 180 cm or 0.4 m

…………………

h) 0.15 kg or 5 g

…………………

…………………

Write each of these sets of numbers in order of size starting with the smallest. a) 0.25 b) 2.6

0.6

0.04

………..

0.65

0.07

0.1

………..

……….

……….

……….

0.3

0.4

………..

……….

……….

……….

………..

……….

……….

……….

c) 0.38

0.56

d) 0.25

0.8

0.52

0.08

e) 1.8

1.08

0.18

0.8

……….

………..

……….

……….

……….

……….

f) Challenge 0.75

0.705

0.77

0.075

0.7

………

………

……..

…….

……..

g) Challenge 0.05 4

0.047

0.1

0.18

0.099

………

………

……..

…….

……..

Write each of these sets of measurements in order of size starting with the smallest. a) 120 cm 12 m

1.5 m

………..

……….

……….

b) 4.5 kg 5000 g

800 g

………..

……….

……….

c) 0.5 l

250 ml

0.06 l

………..

……….

……….

d) 0.6 m

85 cm

0.08 m

9 cm

………..

……….

Change the measurements so that they are all measured in the same unit.

……….

……….

e) Challenge 45 g

0.2 kg

………..

5

………..

0.065 kg

………..

0.02 kg

……….. ………..

Each list of decimals has been written in order of size. Write a possible value for the missing decimal in each list. a) 0.2 b) 0.65 c) 0.8

4

180 g

……….. ………..

0.86

0.3

d) 0

0.7

0.74

………..

0.87

………..

0.1

0.12

e) Challenge 0.189

………..

0.19

0.2

Unit 1A: Number and calculation

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