1. Primary 4 Mathematics Decimals
My Pals Are Here, Book B, Chapter 10: Decimals
Shaping Maths, Book B, Unit 1: Decimals

2. All about Decimals What do you know about Decimals?
Where do you find decimals?
Why do we learn about decimals?
How does Decimal help us in our daily life?

3. Chapter Learning Outcomes
Express tenths as decimals
Express hundredths as decimals
Express thousandths as decimals
Compare and order decimals
Complete number patterns
Round decimals
Convert a fraction to a decimal
Convert a decimal to a fraction

4. Express Tenths as Decimals
The rectangle is divided into 10 equal parts.
Each part represents one tenth.
We write one tenth as or 0.1.
We read 0.1 as zero point one.
0.1 is a decimal.

5. Tenths can be represented on a number line.
Express Tenths as Decimals
Tenths can be represented on a number line.
1 one = 10 tenths

6. Express Tenths as Decimals
Express 27 tenths as a decimal.
27 tenths
We read 2.7 as two point seven.
2 ones tenths =
= 2.7

7. Express Tenths as Decimals
2.7 can be represented as shown.
2 ones 7 tenths = 2.7
2.7 has one decimal place.
Ones 2 7
Tenths
stands for 2 ones
stands for 7 tenths

8. Express Tenths as Decimals
2.7 =
The value of the digit 7 is 0.7.
The digit 7 is in the tenths place.
The value of the digit 2 is 2.
The digit 2 is in the ones place.

9. Express Tenths as Decimals
We can read measurements to one decimal place.
Length of chalk = 3.4 cm
Length of string = 4.8 cm

10. Complete the table below. Fraction Decimal
Let’s Try!
Complete the table below.
Fraction
Decimal
4.3
0.7 kg
42.9 kg m
0.3 m

11. a) In 21.3, the digit ____ is in the tenths place.
Let’s Try!
Fill in the blanks.
a) In 21.3, the digit ____ is in the tenths place.
b) In 16.7, the value of the digit 7 is ____.
c) _____ =
d) _____ = 52.5 3
0.7
5.6 50

12. Let’s Try!
Express as a decimal.
Express as a decimal.
Express 0.6 as a fraction in its simplest form.
Express 1.2 as a fraction in its simplest form.
Express as a decimal in its simplest form.
Express 7 tenths as a decimal.
Express 23 tenths as a decimal.
In 28.3, the value of the digit 3 is _______.
_____ = 1

13. Express Hundredths as Decimals
The square is divided into 100 equal parts.
Each part represents one hundredth.
We write one hundredth as or 0.01.
We read 0.01 as zero point zero one.
0.01 is a decimal.

14. Express Hundredths as Decimals
Hundredths can be represented on a number line.
1 tenth = 10 hundredths

15. Express Hundredths as Decimals
Express 337 hundredths as a decimal.
We read 3.37 as three point three seven.
337 hundredths
3 ones hundredths =
= 3.37

16. 3.37 can be represented as shown.
Express Hundredths as Decimals
3.37 can be represented as shown.
3 ones 3 tenths hundredths = 3.37
3.37 has two decimal places. 7
Ones 3
Tenths
Hundredths
stands for 3 ones
stands for 3 tenths
stands for
7 hundredths

17. Express Hundredths as Decimals
3.37 =
The value of the digit 7 is 0.07.
The digit 7 is in the hundredths place.
The value of the digit 3 is 0.3.
The digit 3 is in the tenths place.
The value of the digit 3 is 3.
The digit 3 is in the ones place.

18. Complete the table below. Fraction Decimal
Let’s Try!
Complete the table below.
Fraction
Decimal
55.65
15.07 litres
0.03
litres m
2.04 m

19. a) In 24.57, the digit ____ is in the hundredths place.
Let’s Try!
Fill in the blanks.
a) In 24.57, the digit ____ is in the hundredths place.
b) In 5.92, the value of the digit 2 is _____.
c) _____ =
d) _____= 19.19 7
0.02
4.63
0.09

20. Let’s Try!
Express 10 tenths as a decimal.
Express 90 tenths as a decimal.
Express 100 hundredths as a decimal.
d) Express as a decimal.
e) Express 0.35 as a fraction in its simplest form.
f) Express 1.28 as a mixed number in its simplest form.

21. We can write money as decimals.
Express Hundredths as Decimals
We can write money as decimals.
$1.00 = ten 10¢
= 100¢
5¢ = $0.05
10¢ = $0.10 $
$ 0.50
$ 0.05
$ 10.00
$ 8.00

22. Express each amount in dollars. a) 65¢ = _____________
Let’s Try!
Express each amount in dollars.
a) 65¢ = _____________
b) 80¢ = _____________
$0.65
$0.80
Express each amount in decimal form.
a) 12 dollars 45 cents = _____________
b) 25 dollars 5 cents = _____________
$12.45
$25.05

23. Express Thousandths as Decimals
of the square is shaded.
Each square is divided into 10 equal parts. Each part represents one thousandth.

24. Express Thousandths as Decimals
We write one thousandth as or
We read as zero point zero zero one.
We write five thousandths as or
We read as zero point zero zero five.

25. 1 hundredth = 10 thousandths
Express Thousandths as Decimals
Thousandths can be represented on a number line.
1 hundredth = 10 thousandths

26. Express as a decimal. Express Thousandths as Decimals = 2.534
= 5 tenths
3 hundredths
4 thousandths
= 2.534

27. Express Thousandths as Decimals
2.534 can be represented as shown.
2 ones 5 tenths hundredths 4 thousandths = 2.534
2.534 has three decimal places. 3
Ones 2 5
Tenths
Hundredths
Thousandths 4
stands for 2 ones
stands for 5 tenths
stands for
3 hundredths
stands for
4 thousandths

28. Express Thousandths as Decimals
2.534 =
The value of the digit 4 is
The digit 4 is in the thousandths place.
The value of the digit 3 is 0.03.
The digit 3 is in the hundredths place.
The value of the digit 5 is 0.5.
The digit 5 is in the tenths place.
The value of the digit 2 is 2.
The digit 2 is in the ones place.

29. Complete the table below. Fraction Decimal
Let’s Try!
Complete the table below.
Fraction
Decimal
0.603
2.034 km km

30. a) In 3.987, the digit ____ is in the thousandths place.
Let’s Try!
Fill in the blanks.
a) In 3.987, the digit ____ is in the thousandths place.
b) In 8.023, the value of the digit 3 is _____.
c) = 1 + _____
d) = _____ 7
0.003
0.03
6.456

31. 3 ones is greater than 2 ones. So, 3.4 is greater than 2.9.
Compare and Order Decimals
Which is greater, 3.4 or 2.9?
Ones 3 4
Tenths
Thousandths
Compare the ones. 2 9
3 ones is greater than 2 ones.
So, 3.4 is greater than 2.9.

32. Which is greater, 2.036 or 2.306? Compare and Order Decimals
Ones 2
Tenths
Hundredths
Thousandths 6
Compare the ones. They are the same. 2 3 6

33. 3 tenths is greater than 0 tenths. So, 2.306 is greater than 2.036.
Compare and Order Decimals
Which is greater, or 2.306? 3
Ones 2
Tenths
Hundredths
Thousandths 6
Compare the tenths. 2 3 6
3 tenths is greater than 0 tenths.
So, is greater than

34. Arrange 0.011, 0.101 and 0.01 in decreasing order.
Compare and Order Decimals
Arrange 0.011, and 0.01 in decreasing order.
Compare the ones. They are the same. 1
Ones
Tenths
Hundredths
Thousandths 1 1 1

35. Arrange 0.011, 0.101 and 0.01 in decreasing order.
Compare and Order Decimals
Arrange 0.011, and 0.01 in decreasing order. 1
Ones
Tenths
Hundredths
Thousandths
Compare the tenths. 1 1 1
1 tenth is greater than 0 tenths.
So, is the greatest.

36. Arrange 0.011, 0.101 and 0.01 in decreasing order.
Compare and Order Decimals
Arrange 0.011, and 0.01 in decreasing order.
Compare the hundredths of the remaining numbers and They are the same. 1
Ones
Tenths
Hundredths
Thousandths 1 1 1

37. Arrange 0.011, 0.101 and 0.01 in decreasing order.
Compare and Order Decimals
Arrange 0.011, and 0.01 in decreasing order. 1
Ones
Tenths
Hundredths
Thousandths
Compare the thousandths. 1 1 1
0 thousandths is smaller than 1 thousandth.
So, 0.01 is the smallest.
In decreasing order, the decimals are , and 0.01.

38. a) Arrange these decimals in decreasing order.
Let’s Try!
a) Arrange these decimals in decreasing order.
21.03, ,
_______ , _______ , _______
21.301
21.03
20.031
b) Arrange these decimals in increasing order.
5.208, 5.828, 5.802
_______ , _______ , _______
5.208
5.802
5.828

39. What is 0.1 more than 3.1? 0.1 more than 3.1 is 3.2.
Complete Number Patterns
What is 0.1 more than 3.1?
0.1 more than 3.1 is 3.2.

40. Look at the number pattern below. What are the next two decimals?
Complete Number Patterns
Look at the number pattern below. What are the next two decimals?
+ 0.1
+ 0.1
+ 0.1
+ 0.1
1.3, , , ______, ______
1.6
1.7

41. What is 0.01 less than 2.34? 0.01 less than 2.34 is 2.33.
Complete Number Patterns
What is 0.01 less than 2.34?
0.01 less than 2.34 is 2.33.

42. Look at the number pattern below. What are the next two decimals?
Complete Number Patterns
Look at the number pattern below. What are the next two decimals?
− 0.01
− 0.01
− 0.01
− 0.01
3.065, 3.055, 3.045, ______, ______
3.035
3.025

43. What is 0.001 more than 0.335? 0.001 more than 0.335 is 0.336.
Complete Number Patterns
What is more than 0.335?
0.001 more than is

44. Look at the number pattern below. What are the next two decimals?
Complete Number Patterns
Look at the number pattern below. What are the next two decimals?
8.2, , , ______, ______
8.203
8.204

45. Fill in the blanks. ______ is 0.1 less than 20.45.
Let’s Try!
Fill in the blanks.
______ is 0.1 less than
______ is 0.01 more than
9.305 is less than ______.
20.35
6.738
9.306

46. Complete the number patterns.
Let’s Try!
Complete the number patterns.
17.12, 17.22, ______, 17.42, 17.52, 17.62
1.605, 1.585, 1.565, ______, 1.525, 1.505
1.20, 1.205, 1.21, 1.215, 1.22, ______
17.32
1.545
1.225

47. Round Decimals A piece of wire is 2.2 m long.
Let’s look at the decimal 2.2 on the number line.
2.2 2 3
2.5
2.2 is between 2 and 3.
2.2 is nearer to 2 than to 3.
2.2 m is 2 m when rounded to the nearest metre.
2.2 m ≈ 2 m

48. Round Decimals A melon has a mass of 1.26 kg.
Let’s look at the decimal 1.26 on the number line.
1.26
1.2
1.3
1.25
1.26 is between 1.2 and 1.3.
1.26 is nearer to 1.3 than to 1.2.
1.26 kg is 1.3 kg when rounded to 1 decimal place.
1.26 kg ≈ 1.3 kg

49. Round Decimals Round 2.735 to 2 decimal places.
Let’s look at the decimal on the number line.
2.735
2.73
2.74
2.735
2.735 is exactly halfway between 2.73 and 2.74.
2.735 is 2.74 when rounded to 2 decimal places.
2.735 ≈ 2.74.

50. Round Decimals When the digit in the tenths place is smaller than 5,6 7
6.1
6.2
6.3
6.4
When the digit in the tenths place is smaller than 5,
the number is rounded down to the smaller whole number. 6 7
6.5
6.6
6.7
6.8
6.9
When the digit in the tenths place is 5 or greater than 5,
the number is rounded up to the greater whole number.

51. Round Decimals
6.1
6.2
6.11
6.12
6.13
6.14
When the digit in the hundredths place is smaller than 5,
the number is rounded down to the smaller tenth.
6.1
6.2
6.15
6.16
6.17
6.18
6.19
When the digit in the hundredths place is 5 or greater than 5, the number is rounded up to the greater tenth.

52. Round Decimals
6.11
6.12
6.111
6.112
6.113
6.114
When the digit in the thousandths place is smaller than 5, the number is rounded down to the smaller hundredth.
6.11
6.12
6.115
6.116
6.117
6.118
6.119
When the digit in the thousandths place is 5 or greater than 5, the number is rounded up to the greater hundredth.

53. the nearest whole number
Let’s Try!
Complete the table below.
Decimal
Rounded to:
the nearest whole number
1 decimal place
2 decimal places
1.404
3.289 kg
2.327 km
8.917 cm
9.995 litres
2.553 g
7.068 1
1.4
1.40
3 kg
3.3 kg
3.29 kg
2 km
2.3 km
2.33 km
9 cm
8.9 cm
8.92 cm
10 litres
10.0 litres
10.00 litres
3 g
2.6 g
2.55 g 7
7.1
7.07

54. Convert a Fraction to a Decimal
I know that
and
How can I convert fractions that do not have denominator 10 or 100 to decimals?

55. Convert a Fraction to a Decimal
Express each of the following as a decimal. a)
Find the equivalent fraction with a denominator of 10 or 100 first.
= 0.5 b)
= 0.06 c)
= 2.04

56. Express each fraction as a decimal.
Let’s Try!
Express each fraction as a decimal. a) b) c) d)
0.12
0.25
7.4
3.46

57. Convert a Decimal to a Fraction
Express each of the following as a fraction or a mixed number in its simplest form.
Write the decimal as a fraction with a denominator of 10 or 100 first and then express it in its simplest form.
a) 0.6
b) 0.28
c) 3.15

58. Let’s Try!
Express each decimal as a fraction or a mixed number in its simplest form.
a) 0.75
b) 3.05
c) 5.25
d) 1.82

59. Express tenths as decimals
Reference — Textbooks
Learning Outcomes
Express tenths as decimals 4B
pp. 53 – 57
pp. 4 – 12
Express hundredths as decimals
pp. 58 – 63
pp. 13 – 20
Express thousandths as decimals
pp. 64 – 67
pp. 21 – 24
Compare and order decimals
pp. 68 – 76
pp. 12, 17, 19, 20, 24

60. Complete number patterns
Reference — Textbooks
Learning Outcomes
Complete number patterns
4B pp. 73 – 74 4B
pp. 23
Round decimals
pp. 77 – 81
pp. 25 – 30
Convert a fraction to a decimal
pp. 82 – 83
pp. 8, 16, 22
Convert a decimal to a fraction
pp. 84 – 85