4 decimals (pg 56-86)

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WAJA MATHS YEAR 4 JPN PERAK

1.Name and write decimals with one to two decimal places.

56

10. Divide decimal of one decimal

place and two decimal places by

a) one-digit number

b) 10

11. Divide decimals by a whole numberwith the dividend value of up to

two decimal places.

12. Solve problems involving division

of decimals

8. Multiply any decimal of one

decimal place and two

decimal places with

a) one-digit number

b) 10, 100, and 1 000

9. Solve problems involving

multiplication of decimals.

1. Name and write decimals with a) one decimal place b) two decimal places

2. Recognise the place value of a) tenths b) hundredths c) tenths and hundredths

3. Convert fractions to decimals of a) tenths b) hundredths c) tenths and

Hundredths vice versa

4. Add any two to four decimals of

one decimal place and two decimal

places involving

a) decimals only c) mixed decimals

b)Whole numbers and decimals

5. Solve problems involving addition

of decimal numbers.

6. Subtract one to two decimals of

one decimal place and two

decimal places involving

a) decimals only

b) mixed decimals

c) Whole numbers and decimals

(mixed decimals)

7. Solve problems involving

Subtraction of decimal.

Learning Outcomes

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Example 1.

Practise reading the decimal numbers below

1. 0.3 - zero point three

2. 0.6 - zero point six

3. 0.89 - zero point eight nine

4. 15.03 - fifteen point zero three

5. 23.48 - twenty-three point four eight.

6 0.4 - ________________________

7. 0.01 - ________________________

8. 4.3 - ________________________

9. 47.28 - ____________________________

Example 2

Write down the number ofdecimal places for each number.

1. 0.8 2. 6.5 8

Number Total number ofdecimal places

6.8 1 decimal place

46.71 2 decimal places

0.3

5.5

23.09

57

Tips5.26 - is read as five point two six

The dot is known as the decimal point.

The number of decimal places of a decimal is thenumber of digits after the decimal point.

1 decimal place 2 decimal places

Lets try

this !!!

After the decimal point read one number at a time

TIPS7 - WHOLE NUMBERA whole number canbe a decimal number

7.0 - 1 decimal place7.00 - 2 decimal

Lets try

this !!!

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Exercise 1 Write the decimals in numerals or in words.

1

Zero point five 2 Zero point nine

3

One point seven 4 Three point eight

5

Eleven point one 6 Zero point nine one

7

Zero point zero five 8 Twenty-four point two six

9

Forty-two point three three 10 Seventy point three nine

1

1

0.6 1

2

0.7

1

3

6.9 1

4

8.8

1

5

5.1 1

6

3.07

1

7

62.35 1

8

50.05

58

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1

9

13.28 2

0

76.86

2. Recognise the place value of : a) tenths b) hundredths c) tenths and hundredths.

Example 1.

The place values and digit values for the decimal 247.38 are as follows.

Whole Number Decimal

point

Decimal Number

Place Value Hundreds Tens Ones Tenths Hundredths

2 4 7 . 3 8

Digit Value 200 40 7 10

3

=0.3

100

8

= 0.08

State the place values of the underlined digit.

1. 14.3 tens (refer the table above)

2. 3.9 ones (refer he table above)

3. 8.75 hundredths (refer the table above)

4. 8.9 tenths (refer the table above)

5. 28.17

6 35.23

59

Points to note:Each digit in a decimal has its

own place value and digitvalue.

TIPSThe place value after thedecimal point ended with

ths

PLACE VALUE OF DECIMAL NUMBERS

A point separates

whole numbers anddecimal numbers

Lets try this !!!

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7. 15.06

Exercise 2

State the place values of the underlined digits.

1. 0.27 2. 6.12

3. 2.47 4. 0.05

5. 51.31 6. 20.20

7. 45.13 8. 47.89

9. 13.98 10

.

37.33

60

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3. Convert fractions to decimals of: a) tenths b) hundredths c) tenths and hundredths and vice versa.

Example 1.

1.10

1= 0.1

2.10

7= 0.7

3.10

3= 0.3

4.10

4=

5.

10

6=

6.10

8=

7.100

3= 0.03

8. 100

7

= 0.07

9.100

19= 0.19

10.100

8=

11100

4=

61

Convert fractions to decimal number.

POINTS TO NOTEA fraction with a denominator of

10 is equivalent to a decimalwith one decimal place.

TIPSDenominator 10

One decimal place

Lets try this !!!

POINTS TO NOTEA fraction with a denominator of100 is equivalent to a decimal

with two decimal places.

TIPSDenominator 100

two decimal places

Lets try this !!!

1 zero

1digit after thedecimal place

2 zeros

2 digits after thedecimal place

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12.100

23=

Example 2.

1. 0.3 =10

3

2. 0.1 =10

1

3. 0.7 =

4. 0.9 =

5. 0.3 =

6. 0.13 =100

13

7. 0.33 =100

33

8. 0.57 =

9. 0.08 =

10. 0.42 =

62

Convert decimals number to fractions.

Lets try this !!!

Lets try this !!!

1 digit after

the decimal point

1 zero

2 digits afterthe decimal place

2 zeros

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Exercise 3

Convert the following fractions to decimal and vice versa.

1.

10

5=

210

9=

3

100

9=

4100

17=

5 100

47

= 6 0.3 =

7 0.7 = 8 0.91 =

9. 0.56 = 10

.

0.02 =

63

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4.. Add any two to four decimals of one decimal place and two decimal places involving

a) decimals only b) whole numbers and decimals c) mixed decimals

Example 1

64

0.6 + 0.1

0.6

+ 0.1

0.7

8 + 0.5

8.0

+ 0.5

8.5

12.3 + 6.6 + 2.41 112.3

6.6+ 2.4

21.3

Arrange in vertical form

according to its place values

Decimal points must be in a

straight line.

Arrange in vertical form.

Decimal points must be in

a straight line.

Arrange in vertical form.


a straight line.

regroup if necessary .

Lets

trythis!!

!

0.7 + 0.2 6 + 2.8 0.2 + 5.3 + 2.9

Arrange the whole number

to one decimal place.

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Example 2

65

0.4 + 0.78

0.04

+ 0.78

0.82

3 + 0.15 + 0.08

3.00

0.15

+ 0.08

3.23

11.1+ 6.6 + 72.41 111.1

6.6+72.4

90.1



straight line


Change the whole number

to two decimal places


a straight line



a straight line

Regroup if necessary.

3.65 + 8.26 20 + 12.63 10.29 + 5.44 + 25 2.9

Lets try this !!!

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Exercise 4

Add the following.

1 0.5 + 0.3 = 2 13 + 0.8 =

3 42.3 + 5.6 + 0.7 4 71.4 + 6.51 =

66

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5 12.46 + 8.17 = 6 17 + 0.7 + 7.82 =

5. Solve problems involving addition of decimal numbers.

1. .1

2. 0.1

3. 0.05

4. 24.26

5. 42.33

6. 70.39

1. or point seven

2. six point nine

3. eight point eight

4. five point one

5. three point zero seven

6. sixty-two point three five

7. fifty point zero five

8. thirteen point two eight

9. seventy-six point eight six

1. 1 decimal place2. 1 decimal place

3. 2 decimal places

4. 2 decimal places

5. 2 decimal places

6. 1 decimal place

2.

3. tenths

4. hundredths

67

EXAMPLE HOW TO SOLVE

EXAMPLE 1

Mazlan weighs 30.4 kg and Wan weighs 0.7 kg more

than Mazlan. What is Wans weight?

Step 1 :

Read and understand question. As you read, underline the

key words.

Mazlan weighs 30.4 kg and Wan weighs 0.7 kgmore than Mazlan. What is Wans weight?

Step 2 :

Write the operation / formula of the keywords signify.

Mazlan weighs 30.4 kg and Wan weighs 0.7 kg

( + )

more than Mazlan. What is Wans weight?

Step 3 : Add

.

0.7 kg + 30.4 kg

0.7 kg

+ 30.4 kg

31.1 kg Answer : 31.1 kg

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Exercise 5

Solve the problems

1

.

A pail holds 2.5lof liquid and a basin holds

3.5 lof liquid. Find the total volume of liquid, in litres, in the two containers.

2

.

.Bottle A contains 1.5 lof syrup. Bottle B contains 2.3 lof syrup and bottle C

contains 0.25 lof syrup. What is the total volume of syrup in the three bottles ?

68

Note : + and are on the same scale. So calculate

as in the order given.

Step 2: Step 3:

RM8000 RM9254

+ RM1254 RM5555RM9254 RM3699

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3

.

The length of three sticks is 3.9 m, 0.87 m and 1.57 m. What is their total length?

6. Subtract one to two decimals of one decimal place and two decimal places involvinga) decimals only b) mixed decimals c) whole numbers and decimals (mixed decimals).

Example 1

69

0.8 0.4

0.8

0.40.4

9 0.58 10

9.0

0.5

8.5

0.7 0.3 0.1

0.7 0.4 0.3 0.1

0.4 0.3


according to its place values.


straight line.



Change the whole number

to one decimal place.(ex.9 = 9.0 )


a straight line.

regroup if necessary




a straight line.

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Example 2

70

2.8 - 0.3 6 - 2.8 9 - 0.5 - 1.4

9.71 - 5.476 11

9.71 5.47

4.24

3.78 2.35

3.78

2.35

1.43

82.08 14.2 9.65 17

82.08 67.88 14.20 9.60

67.88 58.28




straight line





a straight line





a straight line.


Lets try this !!!

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Exercise 6

Subtract the following.

1 0.9 0.3 = 2 19.3 0.8 =

3 20 6.8 3.7 = 4 9 0.57 =

71

0.9 - 0.1 65.9 - 63 16.05 - 3.5 - 2.88

Lets try this!!!

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5 7.64 1.58 0.6 = 6 17 3.7 11.11 =

7. Solve problems involving subtraction of decimal numbers.

7. .1

8. 0.19. 0.05

10. 24.26

11. 42.33

12. 70.39

10. or point seven

11. six point nine


13. five point one

14. three point zero seven

15. sixty-two point three five16. fifty point zero five



7. 1 decimal place

8. 1 decimal place

9. 2 decimal places

10. 2 decimal places


12. 1 decimal place

5.

72


EXAMPLE 1

The length of a stick is 7.5 m. If 3.95 m of the

stick is cut off, what is the length of the stickremains?

Step 1 :

Read and understand question. As you read underline the

keywords.

The length of a stick is 7.5 m. If 3.95 m of the stick is cut

off, what is the length of the stick remains?

Step 2 :

Write the operation / formula the keywords signify.

The length of a stick is 7.5 m. If 3.95 m of the stick is

()

cut off, what is the length of the stick remains ?

Step 3 : Minus.

7.5m 3.95m

7.50 m

- 3.95 m

3.55 m

Answer : 3.55 m

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6. tenths

7. hundredths

Exercise 7

Solve the problems.

1 Yanti bought 10 m of cloth to sew dresses. She used up 8.9 m for her twin

daughters dresses. How much cloth is left?

2 Joseph bought 1.3 lof fresh milk. He drank 0.5 lof it.

What was the volume of milk left?

73


as in the order given.

Step 2: Step 3:

RM8000 RM9254

+ RM1254 RM5555

RM9254 RM3699

Points to notePut a zero to obtain

2 decimal places.

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3 Asmah has a piece of string 14 m long. She cut two pieces, one 3.5 m and the other

5.6 m long. How long is the remaining string?

8. Multiply any decimal of one decimal place witha) one-digit number, b) 10, 100 and 1 000.

Example 1.

Example 2

74

5 6.7 = 33.53

6.7

5

33.5

1. Arrange in vertical form.

2. Place the multiplier below

the last decimal place.

3. Multiply one digit at a time

from right to left.

4. Regroup if necessary.

5. Put the decimal point

according to the decimal

place.

7 2.4 =

Lets try this !!!

1. Arrange in vertical form.

2. Place the multiplier below

the last decimal place.3. Multiply one digit at a time

from right to left.

4. Regroup if necessary.

5. Put the decimal point

according to the decimal

place.

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Example 3

75

5 0.67 = 4.024

0.67

6

4.02

7.8 10 = 78Move the decimal point one

place to the right.

4 0.29 =

3.7 10 = 5.71 100 = 9.197 1000 =

Lets try this !!!

Lets try this !!!

Lets try this !!!

2.3 9 100 = 239

9.5 1 6 1000 = 9 516

Move the decimal point two

places to the right.

Move the decimal point three

places to the right.

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Exercise 8

Multiply.

1 0.3 7 = 2

31.6 10 =

3 16.8 100 = 4 6.2 1 000 =

76

3.03 10 9.22 100 48.3 1 000

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5 4.47 2 = 6 0.45 10 =

7 7.34 100 = 8 8.48 1 000 =

9. Solve problems involving multiplication of decimal numbers.

13. .114. 0.1

15. 0.05

16. 24.26

17. 42.33

18. 70.39

19. or point seven

20. six point nine


22. five point one

23. three point zero seven24. sixty-two point three five




13. 1 decimal place

14. 1 decimal place




18. 1 decimal place

77


EXAMPLE

The mass of a packet of biscuits is 1.25 kg. What is

the total mass of 3 packets of biscuits ?

Step 1 :


key words.

The mass of a packet of biscuits is 1.25 kg. What is the

total mass of 3 packets of biscuits ?

Step 2 :


The mass of a packet of biscuits is 1.25 kg.

( )

What is the total mass of 3 packets of biscuits ?

Step 3 : Multiply

.

1.25 kg 3

1.25 kg

3

3.75 kg Answer : 3.75 kg

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8.

9. tenths

10. hundredths

Exercise 9

Solve the problems.

1 The length of a hockey stick is 68.5 cm. Find the total length of 3 similar

hockey sticks.

2 A bowl can hold 73.4 g of flour. Lina used 6 bowls of flour for baking a cake.

How much flour did Lina use?

78

as n t e or er g ven.

Step 2: Step 3:

RM8000 RM9254

+ RM1254 RM5555

RM9254 RM3699

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3 A tank can hold 13.6 litres of oil when it is full.

How much oil can 6 tanks hold?

10. Divide decimal of one decimal place and two decimal places by : a) one-digit number, b) 10,

Example 1

79

4.6 2 =Arrange in

vertical form

Divide digit by digit from

left to right

2 4 . 6

2 . 3

2 4 .64

0 6

6

0

Lets try

this !!!

Place the decimal point.

in line with decimal point of

dividend

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Example 2

6 7 9 2

80

4.8 4 =

7.92 6 =

Set the time table of 61 = 6

2 = 12

3 = 18

4 = 245 = 30

6 = 367 = 42

8 = 489 = 54

6 7 9 2

.

. Arrange in vertical form.

Place the decimal pointin line with decimal point

of dividend.

.1. 3 2

- 6

1 9

1 8

1 2

- 1 2

0 0

Divide digit by digit

from left to right.


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Example 3

Example 4

81

1.32

Answer

23.5 5 =

0.8 10 =

0.8 10 Move decimal point1 place to the left

TIPS

10 has 1 zero means one move

0.08

34.7 10 =

34.7 10Move decimal point

1 place to the left.

Lets try this !!!

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Exercise 10

Divide

1 6.2 2 = 2 6.5 5 =

3 12.6 6 = 4 4.64 8 =

82

3.47

6.9 10 =

45.3 10 =

27.5 10 =

Lets try this !!!

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5 25.5 10 = 6 13.5 10 =

11. Divide decimals by a whole number with the dividend value of up to two decimal places.

Example 2

5 15 7 0

83

15.7 5 =

Set the time table 51 = 5

2 = 103 = 15

4 = 205 = 25

6 = 307 = 35

8 = 409 = 45

5 15 7

.

. Arrange in vertical form. Place the decimal point

in line with decimal point

of dividend.

.3. 1 4

- 15

0 7

5

2 0

- 2 0

0 0

Divide digit by digit from

left to right.


Put a zero to the dividendwherever there is a remainder

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Exercise 11

Divide.

.

1 10.08 3 = 2 2.28 6 =

3 15.7 5 = 4 18.2 4 =

84

3.14 Answer

18.8 8 =

Lets try

this !!!

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5 69.45 3 = 6 496.4 8 =

12. Solve problems involving division of decimal numbers.

19. .120. 0.1

21. 0.05

22. 24.26

23. 42.33

24. 70.39

28. or point seven

29. six point nine


31. five point one

32. three point zero seven33. sixty-two point three five




19. 1 decimal place

20. 1 decimal place




24. 1 decimal place

85


EXAMPLE

17.7 kg of rice has been divided between three floodvictims. How many kilograms of rice are provided to

each victim?

Step 1 :


keywords.

17.7 kg of rice has been divided between three flood

victims. How many kilograms of rice are provided to eachvictim?

Step 2 :


17.7 kg of rice has been divided between three flood

victims. How many kilograms of rice is provided to

( )

each victim?

Step 3 : Divide

5.9

3 17.7

15

2 7

2 70 0 Answer : 5.9 kg


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11.

12. tenths

13. hundredths

Exercise 12

Solve the problems.

1 The total length of 4 equal pieces of ribbon is 20.08 cm.

Find the length of each piece of ribbon.

2 Roslan packed 6.6 kg of rice into four bags equally.

What is the weight, in kg, of rice in each bag?

86

Step 2: Step 3:

RM8000 RM9254

+ RM1254 RM5555

RM9254 RM3699

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3 Raja pours 9.84 of syrup equally into 8 bottles.

What is the volume, in , of a bottle?

4 decimals (pg 56-86)

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