Chapter 3.pdf - Cambridge University Press

Cambridge University Press • Uncorrected Sample Pages • 2008 © Brookie, Halford, Lawrence, Tiffen, Wallace

SAMPLE

New ZealandCurriculum

Level 3 Number strategiesUse a range of additive and simplemultiplicative strategies with wholenumbers, fractions, decimals andpercentages

Level 4 Number strategies and knowledge

Understand addition and subtraction offractions, decimals, and integersFind fractions, decimals andpercentages of amounts expressed aswhole numbers, simple fractions anddecimalsKnow the relative size and place valuestructure of positive and negativeintegers and decimals to three places

Ordering booksImagine the number of books that areproduced each year and the numberthat are in existence now. In order tocategorise these, a system called theDewey decimal system was invented.For example, 510.12 is a specific codefor books concerned with a particularaspect of mathematics. Books areordered on the shelves in a libraryexactly as decimal numbers areordered, and so a book numbered510.882 is found after books numbered510.12 and will be on the same topic.

A newer form of categorising booksis the ISBN (International StandardBook Number) system. It is a 13-digitnumber that uniquely identifies booksand book-like products publishedinternationally. Each number identifiesa unique edition of a publication, fromone specific publisher, allowing formore efficient marketing of productsby booksellers, libraries, universities,wholesalers and distributors.

Chapter 03.qxd 7/21/08 5:52 PM Page 87


SAMPLE

Do now

Skillsheet

T EACHE R

Mathematics and Statistics Year 988

1 What is the place value of 4 (in words) in the following numbers?

a 2345 b 14 231 c 114

2 Write 1, 132, 15, 2004, 123 in order from smallest to largest.

3 Calculate:

a 34 � 38 b 34 � 46 � 157c 156 � 134 d 421 � 374

4 Find the answers to the following:

a (2 � 8) � 4 b (5 � 3) � 7 c 18 � 3 � 4

5 Estimate the answer for:

a 34 � 270 b 789 � 105c 2765 � 5 d 37 � 212

6 Evaluate:

a 36 � 1000 b 12 000 � 100

7 Estimate the answers to:

a 56 � 4 b 37 � 21c 676 � 4 d 1980 � 12

Prior knowledgeTens Hundreds OnesBEDMAS Decimal point ProductSum Multiply Thousands



SAMPLE

Chapter 3 — Decimals

The decimal system was formed using the base 10 system of whole numbers that we saw inChapter 1.

Which is bigger, 0.09 or 0.2? John says 0.09 is bigger because 9 is bigger than 2. Suesays 0.2 is bigger because hundredths are smaller than tenths.

Then John says, ‘what about 0.29, because that’s got hundredths’. Sue says, ‘0.29 isbigger than 0.2’. Is she right? Why?Place value houses were also investigated in Chapter 1.

Row 1 reads ‘three hundred and twenty-seven thousand, five hundred and eighteen’.

Row 2 reads ‘nine hundred and five thousand, three hundred and eighty’.

If one unit is cut into 10 equal parts each piece is called ‘one-tenth’

If one-tenth is cut into 10 equal parts each piece is called ‘one-hundredth’

If one hundredth is cut into 10 equal parts each piece is called ‘one-thousandth’

� 0.001

The ones/units The tenth/10th The hundredth/100th The thousandth/1000th

�1

1000

�1

100� 0.01

�1

10� 0.1

Thousands

H T O H T O Decimal point

3 2 7 5 1 8

9 0 5 3 8 0

89

3-1 Decimals and place value



SAMPLE


Reading decimals

90

Thousands thousandths

H T O H T O

3 5 7 2 4 1

3

0

t

6

7

5

h

8

2

1

o

5

7 4 3

t h

Row 1 reads ‘three hundred and fifty-seven thousand, two hundred and forty-one pointsix, eight’� 327 241.68 � 357 241 and 6 tenths and 8 hundredths � 357 241 and and

Row 2 reads ‘three point seven, two, five’

� 3.725 � 3 and 7 tenths, 2 hundredths and 5 thousandths � 3 and , and

Row 3 reads ‘zero point five, one, seven, four, three or point five, one, seven, four, three’� 5 tenths, 1 hundredth, 7 thousandths, 4 ten-thousandths and 3 hundred-thousandths

� , , , and 3

100 0004

10 0007

10001

100510

51000

2100

710

8100

610

Key ideas

To write a number with a fractional part we use a decimal point to separate the wholenumber and the fractional part.

The number 0.346 means 3 tenths and 4 hundredths and 6 thousandths, which we canwrite as:

tenths hundredths thousandths3 4 6

� .3 � .04 � .006�3

10�

4100

�6

1000� 3 �

110

� 4 �1

100� 6 �

11000

.3 4 6 .3= .04 .006



SAMPLE

Chapter 3 — Decimals 91

Example 1

ExplanationSolution

What is the value of 5 in 34.457?

For 34.457, the 5 represents5 hundredths.

The value of 5 is � 0.055

100

The 5 is in the hundredths column.

Tens Units . tenths hundredths thousandths

3 4 4 5 7

Example 2

ExplanationSolution

Write these as decimals:

a b c 2 19

10001

27100

31000

a � 0.003

b � 1.27

c � 2.0192 19

1000

1 27100

31000

Example 3

Investigate the set of numbers 1.08, 1.191, 1.092, 1.62, 1.602.

a Which is the biggest number?b Which is the smallest number?c Arrange the numbers in order from smallest to largest.

.

thousandths

1

2

tO

0

2

0

h

0 3

7

1

o

9

t h



SAMPLE


ExplanationSolution

a 1.62

b 1.08

c 1.08, 1.092, 1.191,1.602, 1.62

Write numbers in place value houses.

thousandths

1

1

1

1

1

t

0

1

0

h

8

9

9

o

1

2

t h

6 2

6 0 2

1

1

1

1

1

t

0

1

0

hs

8

9

9

o

1

2

t h

6 2

6 0 2

1

1

1

1

1

t

0

0

1

hs

8

9

9

o

2

1

2

t h

6 0

6 2

3AExercise

1 What is the value of the digit 5?

a 47.5 b 5.132 c 0.357 d 3.615 e 56.46f 347.54 g 30.523 h 65.347 i 0.2357 j 0.354

2 Give the value of the digit in red:

a 26.543 b 37.264 c 389.2d 42.34 e 27.3 f 345.267

1Example

thousandths

thousandths



SAMPLE


g 38.94 h 1.341 i 20.35j 0.2896 k 54.678 l 0.3567

93

3 Write the following as decimals:

a b c d e f

g h i j k l

m n o p q r

4 Write as decimals:

a three units and five tenths b thirty-four units and three hundredthsc fourteen thousandths d twenty-two units and fifteen hundredths

5 Write in words:

a 35.2 b 0.56 c 5.3507 d 4.954003

6 Explore the similarities and differences between:

a 0.5 and .5 b 0.05 and .05 c 10.5 and 0.501

7 In each number, which zero (or zeros) can you leave out without changing the value ofthe number?

a 0.5 b 10.5 c 1.05 d 1.50 e 1.450f 1.405 g 1.070 h 1.700 i 1.003 j 1.3000

8 Find the biggest number in each set of numbers:

a 0.23, 0.32, 0.63, 0.26, 0.36b 0.122, 0.145, 0.169, 0.174c 0.00456, 0.00684, 0.00945, 0.00571

9 Find the smallest number in each set of numbers:

a 0.68, 0.82, 0.12, 0.32b 0.783, 0.258, 0.463, 0.872c 0.0075, 0.00695, 00659, 0.0045

10 Arrange the numbers in each set in order from smallest to largest:

a 1.6, 1.06, 10.6, 0.6 b 2.03, 3.74, 0.366, 1.6c 0.004, 0.142, 0.0123, 0.222 d 0.1211, 0.2111, 0.1121, 0.1112e 6.002, 5.24, 60.20, 53.4, 60.020 f 2.779, 2.007, 27.002, 7.202, 7.002

1724

10002

310

162

1002

71100

2464

10006

5100

14456

100023

910

456100

51000

4661000

481000

27100

13100

6100

5310

510

310

2Example

3Example

11 At Mount Hutt ski resort 0.98 m of snow fell. AtCoronet Peak 0.897 m fell. Which resort had moresnow?

12 The hire of skis costs $24.20, boots $24.00,waterproof pants $22.40 and jacket $20.40.Arrange these costs in order from lowest tohighest.



SAMPLE


13 Matthew went to England as an exchange student. The hours of sunshine for the firstsix days were as shown in the table.

a Which day had the most sunshine?b Which was the dullest day?c Arrange the hours of sunshine in order from smallest to largest.

94

Day 1 Day 2 Day 3 Day 4 Day 5 Day 6

17.26 h 18.26 h 17.05 h 18.09 h 15.34 h 17.62 h

Enrichment: Numbers and value

14 a Using these cards make as many different numbers as you can.i How many different numbers can you make?

ii What is the biggest number?iii What is the smallest number?

b Now add a card with the number three on it and make as many differentnumbers as possible.

i How many different numbers can you make?ii What is the biggest number?iii What is the smallest number?

c Now add a card with the number zero on it and make as many different numbersas possible.


d Now add a second card with the number zero on it and make as many differentnumbers as possible.


1 2

1 2 3

1 2 3 0

1 2 3 0 0

Chapter 03.qxd 7/21/08 5:52 PM 4


SAMPLE


3-2 Adding and subtracting decimals

95

Three students in a Year 9 class all have different methods of working out the same quizquestions that their maths teacher gave them.

The students’ working is as follows:

Marie Charlie Maddy3.6 � 0.78 � 0.78 � ? � 3.63.6 � 1 � 2.62.6 � 0.22 � 2.82

2.6 � 0.22 � 2.82

2.6 � 0.22 � 2.82

With a partner, discuss each method. Can you think of another way of doing the question?Share with your partner. Which method do you prefer?

Key ideas

When adding and subtracting decimals you can use similar strategies to those used whenadding and subtracting whole numbers.For adding and subtracting decimal numbers we can use reversibility, rounding andcompensating, and partitioning.

Example 4

ExplanationSolution

Find the sum of:

a 10.2 and 11.34 using place value b 2.6 � 3.87 by rounding and c 3.41 � 11.2 � 0.098 using place value compensating

a 10.2 � 11.34� 10.2 � 11 � 0.3 � 0.04� 21.2 � 0.3 � 0.04� 21.5 � 0.04� 21.54

b 2.6 � 3.87� 3 � 3.87� 6.876.87 � 0.4 � 6.47

By partitioning, break up 11.34 into 11 � 0.3 � 0.04.Add the whole number 11.Then add 0.3 and 0.04.

By rounding and compensating, add 0.4to 2.6 to make 3 and add to 3.87 to make6.87, and compensate by subtracting the0.4 which we previously added.

0.78

−0.22−2.6

3.61

0.78

0.222.6

3.61 32



SAMPLE

4bExample

5aExample


c 3.41 � 11.2 � 0.0983.41 � 11.2 � 14.6114.61 � 0.098 � 14.61 � 0.09 � 0.008� 14.70 � 0.008� 14.708

Using place value, add the first twonumbers and then add 0.098, but rewriteas 0.09 and 0.008 and add separately to 14.61.

Example 5

a Subtract 3.4 from 8.6. b 5.243 � 2.67

ExplanationSolution:

a 8.6 � 3.4 � 5.2 Using reversibility, 3.4 � ? � 8.6

0.6 � 4.6 � 5.2

3.4

0.64.6

8.64

b 5.243 � 2.675.243 � (2.67 � 0.33)� 5.243 �3 � 2.423� 2.243 � 0.33� 2.573

Using rounding and compensating, add0.33 to 2.67 to make 3 and subtract the3 from 5.243. To compensate add 0.33to 2.243 (we add the 0.33 because wesubtracted 3, which is a larger numberthan 2.67).

3BExercise

4aExample 1 Work out the following by choosing a strategy. Show all your working.

a 12.30 � 6.04 � 3.40 b 16.8 � 2.7 c 18.74 � 6.7d 0.8 � 21.91 e 5.76 � 8.92 f 6.98 � 7.45

2 Work out each sum, showing all your working:

a 3.42 � 1.37 � 0.5 b 0.04 � 2.35 � 34.8c 7.4 � 4.6 � 444.44 d 1.243 � 7.2 � 2.7e 43.8 � 8.25 � 0.43 f 3.423 � 1.85 � 2.461

3 Work out the following by choosing a strategy. Show all your working.

a 25.34 � 15.23 b 324.46 � 21.25 c 7.873 � 6.24d 13.68 � 2.89 e 31.85 � 6.47 f 4.826 � 3.475



SAMPLE


4 Work out these subtractions, showing all your working:

a 5.3 � 2.8 b 4.81 � 1.72 c 12.046 � 7.33d 3 � 0.55 e 12.26 � 10.35 f 11.1 � 4.289

5 Work out the following:

a 2.91 � 32.5 � 2.05 b 3.64 � 2.26 � 12.45c 14.62 � 6.372 � 13.5 d 2024.5 � 1876.436e 15 � 5.475 � 2.22 f 345.6 � 12.76 � 1.547

6 The following times in seconds were recorded in a semi-final of a world series 100 m race:

10.72, 10.31, 10.97, 10.68, 10.76, 10.17, 10.87, 10.35a What is the difference in time between the fastest and slowest athlete?b What is the difference in time between first and second place?

7 Sam biked 1.85 km to Tim’s house. Tim and Sam then biked 2.76 km to the movies in town.

a How far did Sam bike to get to the movies?b How much further than Tim did Sam bike to get to the movies?

8 John has $10.50 in his pocket. If he buys a hamburger with cheese that costs $2.85,how much money will he have left?

9 A family meal of four Kiwi burgers, four small fruit juices, and four small serves of fries ison sale for $37.50. Look at the menu to find how much is saved by buying a family meal.

5bExample

10 Blade works at the local restaurant afterschool. In one week he earned $35.79 andpayed $6.84 in tax. What was his take-home pay?

11 Samantha was given a piano for Christmas. She then purchased a stool for $107.95,some sheet music for $16.60, a music stand for $26 and a candelabra for $7.90.

a What was the total cost?b How much money did she have left from $200?

Today’s Special

KIWI BURGER $5.55

SMALL FRUIT JUICE $2.40

SMALL FRIES $1.90

Enrichment: Do you get the point?

12 John performs the following calculation on his calculator:

He compares his answer to the answers of three of his friends and they are alldifferent. The answers are 2.809, 26.83, 27.316 and 55.576.

a Determine the correct answer.b Discuss the key-stroke errors that were made in the other calculations.

3.14 � 27.23 � 3.054



SAMPLE


John says, ‘All decimals are recurring.’

Sue says, ‘What about ?’

John replies, ‘It is 0.2000000000 . . .’Do you agree? What does John mean by recurring decimals?

15

� 0.2

3-3 Converting fractions to decimals

Key ideas

To change a fraction to a decimal, divide the numerator by the denominator. In changingfrom a fraction to a decimal we often create recurring decimals.

A decimal that repeats is called a recurring decimal and we show the repeating patternusing dots or bars over the numbers.

or and or

Throughout this section you are permitted to use a calculator for any division.Some common fractions that you would have seen already and their decimal equivalents areshown below.

0.2857140.28571428571428 � 0.2#85714

#0.3#

0.33333 p � 0.3

Fraction �numerator

denominator

Fraction

Decimal 0.125 0.2 0.25 0.5 0.6#

0.3#

78

45

34

23

12

13

14

15

18

Essential Mathematics 9 for VELS98

Example 6

ExplanationSolution

Convert the following to decimals:

a b c d27

13

325

38

a

b

c or

d or 0.28571427

� 0.2#85714

#

0.3#1

3� 0.33333 � 0.3

325

� 3.4

38

� 0.375Divide 3 by

Look at the fractional part of the number:

Divide 2 by , so the decimal is 3.4Divide 1 by

Divide 2 by 7 � 0.285714285714285p

3 � 0.3333333333p5 � 0.4

25

8 � 0.375

0.75 0.8 0.875



SAMPLE


Example 7

ExplanationSolution

Convert the following to fractions:

a 0.2 b 0.25 c 2.437

2 represents 2 tenths.

25 represents 25 hundredths.

437 represents 437 thousandths.

a

b

c 2.437 � 2437

1000

0.25 �25100

�14

0.2 �210

�15

3CExercise

1 Convert to decimals:

a b c d e

f g h i j


a b c d e

f g h i j

3 We know that and . Use that information to convert the following

to decimals:

a b c d e f

4 so how many fifths are there in:

a 0.4? b 0.6?

5 Convert to a decimal:

a b c d e

f g h i j 2116

518

1215

1014

612

47

1002

710

51

1004

1100

2110

15

� 0.2

88

78

68

58

48

38

28

� 0.2518

� 0.125

120

34

45

316

3200

1100

58

35

34

25

116

18

15

14

12

7100

710

11000

1100

110

6aExample

6bExample



SAMPLE



a b c d

e f g h

i j k l

7 Convert each set of fractions to decimals and then write the biggest:

a b c d

e f g h

8 Convert to a decimal, rounding your answers to 3 decimal places as necessary.(Calculators may be used).

a b c d

e f g h

9 We know that , so what is the decimal value of:

a b c d

What do you know about ?

10 Convert to a decimal (calculators may be used):

a b c d

e f g h

11 Write to 9 decimal places. What patterns do you notice?

Can you now predict to 6 decimal places?

12 Convert to fractions:

a 0.3 b 0.5 c 0.6 d 0.8e 0.03 f 0.05 g 0.06 h 0.08i 0.23 j 0.35 k 0.46 l 0.58m 0.004 n 0.235 o 3.271 p 4.333

47

, 57

, 67

17

, 27

, 37

557

237

33

222

311

311

17

122

111

66

66

56

36

26

16

� 0.16#

25

123

13

14

153

23

59

712

19

16

1631

, 1250

, 12

211

, 920

, 613

37

, 59

, 23

25

, 19

, 34

510

, 611

27

, 18

35

, 59

25

, 38

334

158

13

1002

35

523

438

325

258

4310

334

214

115

6cExample

6dExample

7Example



SAMPLE


13 Convert to fractions:

a 0.300 b 0.50 c 0.601 d 0.57e 2.47 f 2.40 g 2.44 h 3.08i 0.237 j 1.35 k 4.6 l 0.0021

14 In an archery contest, the best performance is determined by the points scored dividedby the total number of points attempted.

a In the first round Anna attempted75 points and scored 48 points. Inthe next round, she scored 54points and attempted 82 points.Which was the better performance?

b Jean scored 69 out of 95 possiblepoints. Joseph scored 54 out of 80possible points. Who had the betterperformance?

c From 170 points attempted, Peterscored 147 points, and John scored200 from 240 points attempted.Who performed better?

15 Joseph and Alicia played chess on their computers. Alicia said, ‘I have played 38games and beaten the computer 25 times’. Joseph said, ‘I have played 52 games andbeaten it 35 times so I am a better player than you’. Was Joseph correct in saying this?

Enrichment: Decimal patterns

16 a Express and as decimals and use the pattern to predict the decimals for

and Use a calculator to check your predictions.

b Write the decimals for and then predict the decimals for .

Use a calculator to check your predictions.

1599

, 2499

, 9899

199

, 499

, 1299

69

.49

, 59

39

19

, 29



SAMPLE


By using place value houses we can see what happens when we multiply or divide adecimal by 10, or 100, or 1000 and so on.

Consider:

and

A pattern develops:

When multipying by 10, the digits glide 1 place value to the left.When multipying by 100, the digits glide 2 place values to the left.When multilpying by 1000, the digits glide 3 place values to the left.

Multiplication produces a larger value number.

Conversely, when we divide, the digits glide to the right. Division produces a smallervalue number.

Th H T O t h th

54 3

3 154=

÷ 10 1

03 2

2 603=

÷ 100 6

=

÷ 1000

7 10

17

5 4 2

2345=

× 10

Th H T O t h th

3

1 7 4 3

34071=

× 100 0

7 6

67=

× 1000 0

3.4 � 100 � 3403.4 � 10 � 34

34 � 100 � 340034 � 10 � 340

3-4 Multiplying and dividing bymultiples of 10



SAMPLE


Key ideas

When multiplying a decimal by 10 or 100 or 1000 . . . we glide the digits to the left asmany places as the number of zeros.

When dividing a decimal by 10 or 100 or 1000 . . . we glide the decimal point to the rightas many places as the number of zeros.

When multiplying or dividing, an empty ‘cell’ either side of the decimal point is filled witha zero. This shows that there are none of that particular place value.

Example 8

Complete a place value table to help you carry out the following calculations:

a bc d 8.6 � 1004.2 � 1000

3934 � 10000.245 � 10

ExplanationSolution

a Glide digits one place value to theleft when multiplying by 10.

b Glide digits 3 place value to theright when dividing by 1000.

c Glide digits 3 place values to theleft. Because there are no tens orones, zeros are placed in these cells.

d Glide digits 2 place values to theright. Because there are no tenths, azero is placed in the tenths placevalue cell.

a

b

c

d 8.6 � 100

4.2 � 1000

3934 � 1000

0.245 � 10 � 2.45H T O

0

2

t

2

4

h

4

5

th

5

HTH T O

4393

3÷ 1000

t

9

h

3 4

th

HTH T O

4 2

0024= 4200

4.2 × 1000

t h th

HTH T O

8 6

0 8 6= 0.086

8.6 ÷ 100

t h th

Example 9

Complete these calculations:

a b 89.4 � 60000.723 � 400



SAMPLE


8dExample

8bExample

8cExample

9Example

3DExercise

8aExample

ExplanationSolution

a

b

� 0.0149� 14.9 � 1000

89.4 � 6000 � 89.4 � 6 � 1000

� 289.2� 2.892 � 100� 1.446 � 2 � 100

0.723 � 400 � 0.723 � 4 � 100 a Rewrite 400 as and, becausewe can use the doubling

strategy twice.So to multiply by 100, we glide digits 2place values to the left.

b Rewrite 6000 as .Divide 89.4 by 6 (you may use acalculator). So to divide by 1000, weglide digits 3 place values to the right.

6 � 1000

4 � 2 � 2,4 � 100

1 Use place value charts to help find the answers to these calculations:

a b cd e fg h ij k l

2 Use place value charts to help find the answers to these calculations:

a b cd e fg h i

3 Work out the answers to the following:





a b c de f g hi j k lm n o p

6 On average 15.6 mm of rain fell every day for 30 days. What is the total rainfall forthe 30 days?

7 A builder requires 300 m of timber at $4.78 per metre. What is the overall cost?

98.4 � 60000.068 � 1100012.6 � 1200154.8 � 60018.6 � 500062.4 � 1207.94 � 11008.94 � 2000.008 � 700.16 � 40056.7 � 30046.4 � 205.5 � 5027.2 � 503.6 � 2002.6 � 30

0.347 � 100000.003 � 10000.056 � 102.456 � 100345.98 � 10 00081.23 � 10000023 � 10001347 � 101203 � 100017.3 � 1045 � 10380 � 100

0.0579 � 10000.0035 � 1000.24 � 10456.7 � 100017.24 � 10003.7 � 10002.56 � 100567.7 � 10047.467 � 1002.347 � 1036.456 � 101.65 � 10

0.345 � 10004.38 � 100037.54 � 10000.345 � 1004.38 � 10037.54 � 1000.345 � 104.38 � 1037.54 � 10

345.6 � 1 000 0000.7854 � 10 0007.34 � 100 00034.4567 � 100034.4567 � 10034.4567 � 10245.45 � 1000245.45 � 100245.45 � 100.345 � 10000.345 � 1000.345 � 10



SAMPLE


8 Paul paid $156.00 for 400 plastic soldiers. How much was each soldier?

9 A house cost $145 000. If the house is 200 m2, what is the average price per m2?

10 The overall cost of a reception for 70 people was $1071. What was the cost for eachcouple?

11 Tanya buys 3000 sequins for her new dress. If they cost $0.35 per 20 how much do thesequins cost all together?

Enrichment: Standard form and the calculator

12 Large numbers and small numbers are often written in standard form. This is usefulif numbers are too large for the display.

For example, 2 000 000 000 000 can be written as 2 � 1012, meaning the 2 isfollowed by 12 zeros. The calculator shows it as 2 E12 Keys:

0.00000000002 can be written as 2 � 10�11, meaning the 2 is 11 value places afterthe decimal point. The calculator shows it as 2 E�11. Keys:

a What does the E mean?b How many zeros before your calculator changes

to standard form?Start with 1, multiply by 10 and keepmultiplying the answer by 10 until your answerbecomes standard form.

c How many decimal places before your calculatorchanges to standard form?Start with 1, divide by 10 and keep dividing theanswer by 10 until your answer becomes standardform.While in this form we can perform normalcalculations. Here we will considermultiplication and division.For example, is the same as 3 E10 � 5 E�3 or 150 000 000.To write 29, press 2 and X y 9.To write , press 2 and Xy �12.

d Use your calculator to evaluate the following:iiiiiiivvviviiviii 13 000 000 000 000 000 � 0.000 000 000 000 007

0.00 000 000 000 000 12 � 0.000 000 000 03170 000 000 000 000 000 � 14 000 000 000 000 0005 000 000 000 000 � 8 000 000 000 000 0000.000 000 000 000 4 � 0.000 000 000 000 0570 000 000 000 000 � 900 000 000 000600 000 000 000 000 � 0.000 000 000 000 035 000 000 000 000 � 0.000 000 000 04

2� 12

30 000 000 000 � 0.005

)EXP2(

)12EXP2(

�11



SAMPLE


3-5 Multiplying a whole number by anumber less than one

A carpenter needs three pieces of timber 0.4 m long.

Will he need more than 3 m of timber? Discuss this with your partner.What does this tells us about multiplying a whole number by a number less than one?Discuss.

Key idea

When multiplying by a number less than one, the answer is smaller than the whole number.

Example 10

ExplanationSolution

Work out the answer: 4 � 0.3

Multiplying by 2 andthen multiplying 2 againis the same asmultiplying by 4. � 1.2

� 2 � 0.6

4 � 0.3 � 2 � 2 � 0.3

0.3 0.6

× 4

×doubledouble

0.3 4

1.2

Example 11

Evaluate: .5 � 0.6

ExplanationSolution

Using the double/halve strategy:double 5 and halve 0.6glide one place to the left� 3

� 10 � 0.35 � 0.6

10Example

3EExercise

1 Evaluate:

a b c de f g h 34 � 0.316 � 0.721 � 0.512 � 0.8

9 � 0.43 � 0.87 � 0.65 � 0.5



SAMPLE


11Example 2 Evaluate:

a b c de f g h

3 Pere requires 7 pieces of decking timber to make steps. Each piece must be 0.75 mlong. What length of timber will he need?

4 Wiremu has been asked to tie the flowers in the garden to stakes. He uses 0.48 m lengthsof twine. How much twine will he have to buy if there are 23 flowers to be tied?

5 A 10-cent coin is 0.013 m in diameter. A coin trail for 10-cent pieces is used to helpraise funds for a class trip. How long will the trail be if there are 250 coins?

6 Tilly drinks 0.33 L of milk each morning. How much milk does she drink in a week?

7 Each of Sam’s cows drinks 23 L of water every day. He adds 0.17 L of dissolvedminerals for every litre of water that they drink. If he has 10 cows, what quantity ofdissolved minerals must he add every day?

8 Pani decides to buy her friends some chew bars. She buys 4 coconut, 8 caramel,3 chocolate and 7 peppermint bars. How much will she spend?

5 � 0.1089 � 0.0047 � 0.194 � 0.074 � 0.926 � 0.7 98 � 0.353 � 0.86

Tempting TimesCoconut delights $0.55Chewy caramels $0.72Chocolate puffs $0.38Peppermints $0.25

Enrichment

9 Evaluate:

a b c de f g h

10 Terry built a small ramp to use with his skateboard.He used 0.58 m of plywood for the slope and 0.32 mfor the rise. His friends were so impressed that hewas asked to make another seven ramps. Eachpiece of slope plywood costs $0.82 and each piece of rise plywood costs $0.55.

a How much plywood is required for seven slopes?b His friend Parekura has sufficient plywood for three rises and two slopes and will

provide it for no cost. What is the total length of plywood supplied by Parekura?c What length of extra plywood is required for the rises?d What length of extra plywood is required for the slopes?e What is the total cost of the ramps Terry builds?

52 � 0.00742 � 0.42126 � 0.10321 � 0.2414 � 0.8618 � 0.0515 � 0.4211 � 0.78

0.32 m0.58 m



SAMPLE


Most real data is in decimal form andcalculations often arise that involve the useof these decimal fractions.

From the table, what does the time takento travel around the Sun tell you about theposition of the planets from the Sun? Whichplanet is closest to the Sun? Which planet isthird closest?

Often, calculations involving decimalsrequire multiplication; for example, howlong does it take Saturn to orbit the Sun fivetimes?

3-6 Multiplying decimals

Time taken to orbit the SunPlanet Period of revolution

(years)

Key ideas

When multiplying decimals:

Determine how many decimal places there are in each number.

Perform normal multiplication.

Write your answer to the total number of decimal places in the question.

Example 12

ExplanationSolution

Calculate:

a b 2.42 � 3.33.24 � 2

a Rewrite the decimal as a whole number.Use multiplication strategy to solve.3.24 � 324 � 100Divide through by 100.

b Rewrite decimal as whole numbers:2.42 � 242 � 100 and 3.3 � 33 � 10.Use a multiplication strategy to solve 242 � 33 � 7986Divide through by 100 and 10.

a� 324 � 100 � 2� 324 � 2 � 100 � 648 � 100 � 6.48

b 2.42 � 3.3� 242 � 100 � 33 � 10� 242 � 33 � 100 � 10� 7986 � 100 � 10� 7.986

3.24 � 2

� 200 40 230 6000 1200 603 600 120 6



SAMPLE


Example 13

ExplanationSolution

Calculate:

a b 3.678 � 900.2 � 0.4

a Rewrite decimal as a whole number:0.2 � 2 � 10 and 0.4 � 4 � 10Use multiplication strategy to solve 2 � 4 � 8.Divide through by 10 and 10, or 100.

b Rewrite numbers as whole numbers and use a multiplication strategy to solve 3678 � 90 � 331 020.Divide through by 100 and 10, or 1000.If the last digit is zero it can be removed as ishas no place value.

a� 2 � 10 � 4 � 10� 2 � 4 � 10 � 10� 8 � 10 � 10� 0.08

b� 3678 � 1000 � 90� 331 020 � 1000� 331.020 or 331.02

3.678 � 90

0.2 � 0.4

3FExercise


a b c de f g h

2 Multiply the following:

a b cd e fg h i


a b c de f g h


a b c de f g h

5 Find the product of each pair of numbers:

a 1.2, 0.02 b 8.6, 0.01 c 0.2, 0.8d 2.3, 3.6 e 3.4, 2.7 f 5.4, 7.7g 32.24, 2.3 h 16.5, 12.04 i 4.13, 2.22

2.67 � 5001.4 � 3002.735 � 2003.14 � 1004.2 � 203.5 � 402.74 � 503.74 � 70

6.45 � 0.77.93 � 0.44.31 � 0.52.34 � 0.60.2 � 0.40.7 � 0.70.4 � 0.30.2 � 0.5

3.4 � 47.245.2 � 9.426.5 � 8.37.9 � 5.24.6 � 2.79.3 � 4.25.3 � 6.23.6 � 5.87.3 � 2.4

3.42 � 69.54 � 94.67 � 63.73 � 87.1 � 75.2 � 43.3 � 32.4 � 2

12aExample

12bExample

13aExample

13bExample



SAMPLE


Enrichment: Modular kitchens

14 The cost of a modular kitchen is decided by the numberand type of cabinets required.Tim and Mary require six normal cupboards costing$89.70 each, three sets of drawers costing $105.30a set, one sink unit costing $126 and two cornerunits costing $99.95 each.

Packages are also available:

Package 1: 4 cupboards, 2 drawers and a sink unit for $680

Package 2: 5 cupboards, 3 drawers and a sink unit for $800

Package 3: 6 cupboards and 2 drawers for $900.

a Calculate the overall cost if Tim and Mary buy each component separately.b Calculate the cost if they use each package and buy the extra pieces needed.c What is the cheapest way for Tim and Mary to buy their kitchen?

6 Use your calculator to find the answer and then round your answers to the nearestdollar:

a b cd e fg h i

7 Use your calculator to find the answer and the round your answers to the nearest cent:

a b cd e fg h i

8 Paula needs seven pieces of timber, each 6.8 m long.

a What is the total length needed?b Determine the total cost if the price of the timber is $4.20 per metre.

9 A new water tank can store 750 litres of water. The average water collected in the tankis 1.75 litres per day. Will the tank fill to capacity over a year if no water is removed?If so, how much excess water will there be?

10 David earns $5.67 per hour as an apprentice. If he works38.3 hours, how much will he earn?

11 A timber supplier purchases 47 m of timber at $2.75 permetre and then sells it for $4.36 per metre. How muchprofit is made?

12 A plumber requires 18.57 m of drainage pipe. If the pipesells at $2.78 per metre, how much will it cost?

13 A fireplace requires 800 bricks, which weigh 0.60 kg each. Can the builder use histruck to carry them if the truck takes a maximum load of 500 kg? Explain your answer.

$100.01 � 345.45$3.58 � 401.423.568 � $23.300.23 � $35.24$116 � 0.04350.45 � $22.98$34.32 � 22$0.34 � 26312 � $23.20

34.2 � $6.125.9 � $142.6 � $3.4612 � $10.6717 � $6.105 � $5.157 � $6.254 � $8.503 � $2



SAMPLE


3-7 Dividing a whole number bya number less than one

Division introduces more language. The number you are dividing by is called the divisor.The answer is called the quotient. When you divide 20 by 4, the divisor is 4 and thequotient (answer) is 5.

When we divide 10 by 2, we can change the problem to multiplication and say: ‘What doI multiply 2 by to give me 10?’

�

There are 5 lots of 2 in 10 whole.

When we divide by a decimal less than one, we can carry out the same operation:

becomes �

Q: How many ‘lots of’ 0.2 are there in one whole?A: 5

This means:

For the equation �, it becomes �

We can use three deci-strips.

Q: How many ‘lots of’ 0.2 are there in 3 whole?A:

This means: If we divide by a decimal less than one with 2 decimal places, we could divide 1 whole

into 100 cells, each with a value of 0.01, and carry out the same process:

�, which becomes �

Q: How many lots of 0.02 are there in one whole?A: 50

This means: 1 � 0.02 � 50

� 10.2 �1 � 0.02 �

3 � 0.2 � 15

3 � 5 � 15

� 30.2 �3 � 0.2 �

1 � 0.2 � 5

� 10.2 �1 � 0.2

10 � 2 � 52 � 5 � 10

� 102 � 1 2 3 4 7 85 6 9 10

10 whole

.1

.1.1

.2

.1

.3 .4 .7 .8.5 .6 .9 1.0

1 whole.1 .1 .1 .1 .1 .1 .1

1

1 whole.1.1 .1 .1 .1 .1 .1.1 .1 .1

2 3 4 5

1

2

3 whole

1 2 3 4 5



SAMPLE


If we had 3 whole and wished to divide by 0.02, there would be lots of 0.02:

or

Use your calculator to solve �. It gives � .

Q: How many lots of 0.002 are there in 1 whole?A: 500

Q: How many lots of 0.002 are there in 3 whole?A: 1500

Have a look at all the examples we have calculated. What happens to the quotient(answer) as the value of the divisor becomes smaller and smaller?

� 5001 � 0.002 �

3 � 0.02 � 1503 � 50 � 150

3 � 50

Key ideas

A division equation may be changed to a multiplication equation.

The smaller the divisor the larger the quotient (answer to a division equation).

Make the divisor a whole number by gliding the place value to the left.Do the same for the whole number.For example: is the same as

Estimate the answer to a division equation to check that it is sensible.400 � 34 � 0.03

Example 14

ExplanationSolution

Calculate:

a b c 8 � 0.0049 � 0.034 � 0.2

Make the divisor into a whole number by gliding thedigits for both numbers one place value to the left.

How many ‘lots of’ 2 are there in 40?

a� 40 � 2� 20

4 � 0.2

H O

4

04

t

0

0

h

0

H O

2

t

2

h



SAMPLE


ExplanationSolution

The divisor is made into a whole number by gliding thedigits for both numbers two place values to the left.

The divisor is made into a whole number by gliding thedigits for both numbers three place value to the left.

So we can now ask: ‘How many ‘lots of’ 4 are there in 8000?’

b

� 300� 900 � 39 � 0.03

c

� 2000� 8000 � 48 � 0.004

TH O

3

t

0

h

3

TH O

009

t

09

h

0

THTh O

4

t

0

h th

0 4

THTh O

0008

t

08

h th

0 0

Example 15

ExplanationSolution

Evaluate: 51 � 0.17

Make the divisor into a whole number by gliding thedigits of both numbers two place values to the left.How many lots of 17 are there in 5100?(Remember: )3 � 17 � 51

� 300

51 � 0.17 � 5100 � 17

Example 16

For these calculations, estimate the quotient and then use your calculator to check youranswer:

a b c 11 � 0.4375 � 0.123 � 0.4

So we can now ask: ‘How many ‘lots of’ 3 are there in 900?’



SAMPLE


14aExample

14bExample

14cExample

15Example

ExplanationSolution

Glide both numbers one place value tothe left. Q: What number multiplied by 4gives an answer close to 30? A: 30 is halfway between 28 and 32 so the quotient isthus half way between 7 and 8.By calculator: 7.5....Glide both numbers two place values tothe left. Q: What number multiplied by12 gives an answer close to 500?A: thus ,which is very close to 500.By calculator: 41.66666 . . .Glide both numbers three place values tothe left. Q: What number multiplied by437 gives an answer close to 11 000? A: 437 is close to 500, and � 11 000 or By calculator: 25.171... Round sensiblyto 2 decimal places.

11 000 � 500 � 22500 � 22

40 � 12 � 4804 � 12 � 48

aand

A sensible estimate would give aquotient between 7 and 8.Calculator quotient

b

A sensible estimate would give aquotient a little larger than 40.Calculator quotient (2 d.p.)

c

A sensible estimate would give aquotient a little larger than 22.Calculator quotient

(2 d.p.)� 25.17� 25.17162471

� 22� 11 000 � 50011 � 0.437 � 11 000 � 437

� 41.67

40 � 12 � 4805 � 0.12 � 500 � 12

� 7.5

4 � 8 � 324 � 7 � 283 � 0.4 � 30 � 4

3GExercise


a b c de f g hi j k l



3 Find the answer:

a b c de f g h

4 Work out the answers:

a b cd e fg h i 18 � 0.0938 � 0.1935 � 0.25

144 � 0.2456 � 0.2848 � 0.4842 � 0.0736 � 0.1226 � 0.13

8 � 0.0056 � 0.0044 � 0.0089 � 0.0017 � 0.0023 � 0.0032 � 0.0085 � 0.005

9 � 0.096 � 0.039 � 0.067 � 0.077 � 0.054 � 0.046 � 0.043 � 0.124 � 0.083 � 0.062 � 0.054 � 0.04

126 � 0.948 � 0.345 � 0.5346 � 0.249 � 0.736 � 0.924 � 0.612 � 0.34 � 0.29 � 0.38 � 0.43 � 0.3



SAMPLE


16aExample

16bExample

16cExample

5 i Show your working to estimate the quotient.ii Use your calculator to find the answer, then round sensibly.

a b cd e fg h i


a b cd e fg h i


a b cd e fg h i

8 Sally buys 15 m of ribbon for giftwrapping small parcels. She uses 0.37 m of ribbonfor each parcel. How many parcels can she wrap? (Show your working.)

9 Tinesia is making bookshelves, and her local timber merchant sells timber shelving in6 m lengths. If her shelves are 0.55 m long, how many can Tinesia make from eachlength of timber? (Show your working.)

10 Hone cuts firewood into 0.375 m lengths.

a How many pieces does he get from a tree trunk 8 m long?b How long is the short leftover piece that can be used for kindling?

5 km � 0.22812 cm � 0.63910 kg � 0.5343 g � 0.0274 t � 0.23215 cm � 0.1764 m3 � 0.1148 L � 0.1937 kg � 0.251

5 kg � 0.898 L � 0.4814 cm � 0.716 m2 � 0.197 km � 0.3715 m � 0.123 t � 0.148 m � 0.94 L � 0.25

6 km � 0.88 Hz � 0.75 g � 0.612 L � 0.97 tonnes � 0.718 L � 0.19 cm2 � 0.41 m � 0.64 kg � 0.7

Enrichment: Outdoor camp

11 Rimu College is running an outdoor camp for the students. Find the maximumnumber of students who could attend this camp.Food for each student has been calculated as follows:

Meat: 0.125 kgPotatoes: 0.12 kgVegetables: 0.235 kgFruit: 0.345 kg

The cook buys 20 kg sausages, 45 kg potatoes,

32 kg fruit, and 18 kg of cabbages.

Four manuka tent pegs, 0.375 m long, are required for

each three-person tent. They are cut from 2 m long manuka stakes. Liz provides 65

stakes. There can be fewer than three students in a tent.

The number of students permitted to attend the camp is restricted by the area of

the bathrooms, which are 42 m2. There must be 0.72 m2 per student at the camp.



SAMPLE


3-8 Dividing decimalsDivision of a decimal number by another decimal number simply means that we are usingnumbers with more digits to carry out the division. We need to know what we are doing andif the answer obtained is sensible. Calculators help speed up the process, but we need tounderstand what is happening in the division problem.

Key ideas

Glide the last place value of both numbers to the left by the same number of places sothat the divisor becomes a whole number.

Estimate the quotient.

Use the calculator and check the answer against your estimate.

Example 17

ExplanationSolution

Calculate: 185.4 � 1.06

Digits of the divisor glide twoplace values to the left.Digits of the other number alsoglide two place values to the left.

Round 18 540; round 106.Divide 20 000 by 100.

Calculator: quotient is close to 200.Round sensibly (2 dp).

Calculator quotient Sensible quotient (2 dp)� 174.91

� 174.9056604� 200� 20 000 � 100� 18 540 � 106185.4 � 1.06

OT TH O

601

t

01

h

6

HOT T

4581

O

0

t h

4581



SAMPLE


3HExercise

Enrichment

7 Jason is interested in the profit he will receive when he sells some cattle from his farm.He sells them for $2679.89. The beef schedule pays him $0.301 per kilogram. Heknows that feed costs $3.072 per 100.75 kg of beef produced. Other production costsare shown in this chart.

Item Cost per x kg of beef producedWages $4.208 per 47.9 kgFencing $1.008 per 25.607 kgVet, medicines, drenches $0.157 per 60.23 kg

Use this information to calculate his profit.

17Example 1 Calculate using gliding place values and estimation before using your calculator.Round the quotient sensibly.


2 Calculate using gliding place values and estimation before using your calculator.Round the quotient sensibly.

a bc de f

3 One dress takes 2.56 m of material. How many dresses could be made from 120.45 mof material?

4 Jerry travels 456.78 km in 8.06 hours. What is his average speed?

5 Star Hospital allows $2.017 for food per patient each day. If the budget allows $2508per day, how many patients can be provided with food?

6 Petrol costs $1.8694 per litre. William spends $87.04 to fill his car’s petrol tank. Howmuch petrol did he buy?

516.1 kg � 21.75298.32 L � 5.608207.6 m2 � 4.033.456 tonne � 2.11345.8 km � 0.5512.78 m � 1.3

2.1 � 1.07247 � 2.00853.471 � 1.509468.06 � 2.482687 � 9.5163.8 � 4.93143 � 3.561.03 � 0.0568.23 � 7.5567 � 12.627.3 � 3.412.34 � 1.2



SAMPLE


Decimals are used widely in everyday life, as seen in previous exercises. When performingoperations with decimals in everyday situations, we often get answers that have no realmeaning.

For example, consider an answer of $18.987. We normally round this to $18.99. Then weround it to $19.00 if we are calculating the cost of something, because the smallest coin weuse is 10 cents. So, when calculating problems involving money, we always need to checkhow sensible our solution is.

When solving more difficult problems, it helps to break them into steps.

3-9 Applications of decimals usinga calculator

Key ideas

Steps for solving problems:

1 Understand the problem. What am I given and what am I asked to find?2 Decide on a method.3 Write a mathematical statement.4 Estimate the answer if necessary.5 Determine your answer.6 Check that the answer is sensible and round off if necessary.

Example 18

ExplanationSolution

Fran orders 26 packs of 33 mini pizzas for a fundraisingevent. She purchases each pack for $17.58 and sells thepizzas individually. She wishes to raise $300.

a What is the total price for the packs of pizzas?b For how much should each mini pizza be sold?

Cost per pack number of packs

Number of packs number of pizzas in a packThis is the total revenue to be raised.Total revenue number of pizzasRound to the nearest 10 cents.

�

�

�aThe total cost is $457.08.

b

Each mini pizza would sell for 90cents.

$757.08 � 858 � $0.882377622$457.08 � $300 � $757.0826 � 33 � 858

$17.58 � 26 � $457.08



SAMPLE


Pizza menu Small Large Family Pasta menu Entree MainMarguerita $4.90 $8.20 $10.90 Spaghetti marinara $5.50 $8.90Kiwi $5.80 $9.40 $12.30 Chicken carbonara $6.50 $9.50Hawaiian $5.80 $9.40 $12.30 Lasagne $7.90Volcano $5.80 $9.40 $12.30Napoli $5.80 $9.40 $12.30 Extra pizza toppings will be charged forUsual $5.50 $8.80 $11.80 60c small 80c large $1.00 familyMelton Special $6.30 $9.90 $12.70Americana $5.80 $9.40 $12.30 Garlic breadMushroom $5.80 $9.40 $12.30 $4.30 small $6.30 large $7.50 familyRocky’s Special $6.90 $10.60 $13.90 Garlic pizza pastry (One size only) $3.80

3IExercise

Everyone has ordered a meal at one time or another. But have you ever thought about howmuch mathematics is involved? Look at the copy of the menu from Rocky’s Restaurant belowand use it to help you answer the questions that follow.

1 What is the cost for each of these orders?

a A small Hawaiian pizza with extra green olivesb A family size Volcano pizza and a small Americana pizzac A large Napoli pizza with extra mushrooms and a small Kiwi pizzad A family size Mushroom pizza with extra bacon and a large Marguerita pizzae A small Rocky’s Special pizza with pineapple, and a garlic pizza pastry

2 The Scott family orders a main spaghetti marinara for Kaylene, lasagne for Matthew, asmall Rocky’s Special pizza with pineapple for David, a large Kiwi pizza forChristopher and a small Hawaiian pizza for Samantha, with a side order of garlicpizza pastry. How much will the meal cost and what is the average price per person?

3 Rocky purchases ham at $15.00 a bag. Each bag contains 6 kg of sliced ham pieces.On average he can use this ham on 30 Kiwi pizzas. How much ham is used on eachpizza and what is the cost per pizza for the ham only?

4 A Melton Special is the same as a Usual pizza with two extra toppings, but a Melton Specialcosts less. How much cheaper is a small Melton Special than the equivalent Usual pizza?

5 If 15 people each gave you $5.00 to purchase as many large pizzas as you could andreceive the least charge possible, what would you order?

18Example

Enrichment: Pizza and pasta

6 The Year 7 students at Rimu College have a ‘pizza and pasta’ day on the last day ofterm. Rocky charges $6.00 for chicken carbonara, $6.50 for lasagne and $5.00 forany small pizza. The local supermarket sells drinks for $8.40 per dozen.

a If 80 students choose pizza, 20 choose lasagne and 29 choose chickencarbonara, and each student has one drink, what is the overall cost of the day?

b Each student is to be charged the same amount. How much will each student pay?



SAMPLE


W O R K I N G

BuildingAndrea wished to build a wardrobe for her bedroom and wondered if she could afford to doit with the $100 she had saved. The panelling costs $14.60 per square metre and comes insheets of different sizes. The glue, nails and hinges cost $15.50 in total. The design is shown below. The two doors are the same size and there is no back on the wardrobe.

Calculating1 Complete the table below.

22 Can Andrea afford to build the wardrobe?

ModifyingAndrea decided to modify her wardrobe so that the partition andthe shelves are only 15 cm wide.How much money will she save using this new design?Can she afford to build it?

Improving and comparing1 1 Can you use the same guidelines to design a wardrobe that

has more space than Andrea’s?2 2 Find out the sizes of panelling sheets and decide which sheet sizes have minimal

wastage, and so improve your costing calculated in Question 1.3 3 Compare the cost of Andrea’s wardrobe to the cost of some readymade wardrobes.

Decimals

200 cm

220 cm20 cm

40 cm180 cm

partition

Item Size (cm) Area (m2) CostSide 0.2 � 2.0 � 0.4SidePartitionBaseTopDoorDoorShelfShelfShelfNails, glue and hinges $15.50

20 � 2000.4 � $14.60 � $5.8420 � 200

Total cost

40 cm

15 cm

Mathematically



SAMPLE

121Chapter 3 — Decimals

Using technology to set up spreadsheetsSpreadsheets are very useful when you are doing repetitivecalculations or wish to vary values and not calculate the answereach time. Fionna wishes to buy figurines. Some are made oflead and cost $15.40 each and some are made of plastic, andcost $6.47 each. She needs to purchase eight figurines of anytype to complete her set and can spend no more than $100.

Setting up the spreadsheetTo help Fionna find out what combinations of the numbers of figurines to buy, set up aspreadsheet.1 Complete columns A and B, ensuring that the total number of figurines is eight.

2 2 Determine the rule you will use to calculate the total in:a C2 b D2 c E2

3 3 Enter these in the table and then use the Fill Down operation to complete columnsC, D and E.

Using the spreadsheetWhich combinations of the numbers of lead and plastic figurines are possible for Fionna to buy?

Modifying the spreadsheet1 1 Suppose Fionna’s friend Tomika has $50 to spend. Set up a spreadsheet to determine

how many different combinations of figurines she could afford to buy.2 2 If Fionna and Tomika combined their resources, set up a spreadsheet to determine:

a the maximum number of figurines they could buyb the minimum number of figurines they could buy if they spent most of the

money.c If a new set consisted of a minimum of two lead and a minimum of seven plastic

figurines, could they each buy a set?d What are the possible combinations of each set if both Fionna and Tomika buy the

same sets?ary

A B C D E1 No. of No. of Total cost Total cost Total cost

lead plastic of lead of plastic offigurines figurines figurines figurines figurines

2 0 8

3 1 7

4 2 6

5 3

6

7

FPO



SAMPLE

Rev

iew

122

1 What is the value of 4 in 3.042?

2 Express as a decimal.

3 Write the numbers 0.023, 2.358, 5.23, 2.3 in order from smallest to largest.4 Find the answer to .5 Find the answer to .6 Find the answer to 0.4 � 0.02.7 Find the answer to 28 � 0.04.8 Write this decimal fraction in words: 34.703

6 � 0.236.45 � 1000

1100

Chapter summaryDecimals

Decimals7.346 means 7 units, 3 tenths, 4 hundredths and 6 thousandths.To convert a fraction to a decimal, divide the numerator by the denominator.

RoundingRound down if the next number is less than 5: to one decimal place.Round up if the next number is 5 or more: to two decimal places.

Addition and subtraction of decimalsUse place value houses.Add or subtract whole numbers.Write decimal fraction as fraction, and write in place value house.Add or subtract the same place value digits.Change the fraction back to a decimal.

Multiplication and division of decimalsTo multiply by 10 or 100 or 1000, glide the place value to the left the same number ofplaces as there are zeros.To divide a decimal by 10 or 100 or 1000, glide the place value to the right the samenumber of places as there are zeros.To multiply decimals by decimals:1 Change decimals to whole numbers.2 Use multiplication strategies to solve.3 Divide through by the multiples of 10 used to convert to the decimals.To divide a whole number by a decimal, glide the place value to the left the samenumber of places for both numbers, to make the divisor a whole number. Carry out thewhole number division.To divide a decimal number by another decimal, glide the place value to the right forboth numbers the same number of places, to make the divisor a whole number.Estimate your answer. Carry out the calculation on the calculator and round sensibly.

32.1356 � 32.143.131 � 3.1


Short-answer questions



SAMPLE

Review

123

9 Estimate the total cost, using leading digit estimation:one dog roll at $2.98 and 3 kg of washing powder at $1.57 per kg

10 Find the answer to:

a

b11 Find the answer to:

a

b

c12 Find the answer to:

a

b

c13 Find the answer to:

a

b

c14 At a sale DVDs cost $19.50 each and CDs cost $14.95 each. What is the total cost of

three DVDs and three CDs?15 A cardboard box has a mass of 0.37 kg. When filled with drink bottles it has a mass of

21.25 kg. How many bottles, each weighing 0.87 kg, are in the carton?16 Mark saved $20 to go to the grand final of his District League. His return fare cost

$6.35, his ticket was $8.00, a football record was $2.50 and his food cost $1.55.

a How much did it cost him for the day?

b How much money did he have left from his $20?1

1 A bottle contains 250 mL of medicine. You are required to take 0.8 mL three times per day.

a How many equal doses will you get from a bottle?

b How long will the bottle last before you need a new one?

c How much will be left in the bottle at the end?2 Pauline has $300 to spend at the shopping mall. She purchases five photo frames at

$29.55 each and six CDs for $18.35 each.

a How much did she spend on photo frames?

b How much did she spend on CDs?

c How much did she spend altogether?

d How much did Pauline have left after these purchases?

18 � 0.04

123 � 0.3

3 � 0.01

4 � 0.26

3 � 0.004

2 � 0.32

2.94 � 13.7 � 6.23

48.37 � 26.016

12.32 � 6.45

50 � 0.5

0.245 � 4000


Extended-response questions



SAMPLE

Chapter 3.pdf - Cambridge University Press

Documents

Transcript of Chapter 3.pdf - Cambridge University Press