1. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Working with decimals
Decimal Scales
Rounding to 1 decimal place
Addition and Subtraction
Multiplying by a single digit
Dividing by a single digit
Multiplying by 10, 100, 1000
Dividing by 10, 100, 1000
Converting length
Converting Volume
Converting Weight
19-Apr-17
Created by Mr. Lafferty Maths Dept.

2. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
19-Apr-17
Created by Mr. Lafferty Maths Dept.

3. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Writing Decimals
Learning Intention
Success Criteria
1. To explain what a decimal number is. Write down the decimal number represented by a fraction diagram.
Understand what a decimal number is.
2. Write down the decimal number represented by a fraction diagram.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

4. Decimal Numbers www.mathsrevision.com means ten Writing Decimals
National 4
NUM 1.2
Writing Decimals
When you take a single unit
and divide it into 10 bits,
what we then have are
decimal fractions of a whole number
Imagine, 1 bar of chocolate as our UNIT of measure.
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
or 0.1
19-Apr-17
Created by Mr. Lafferty Maths Dept.

5. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Writing Decimals
Example : Write down the decimal number
represented by the shaded area.
(a)
(b)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

6. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Writing Decimals
Example : Write down the decimal number
represented by the diagram.
(a)
(b)
(c)
(d)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

7. Decimal Numbers www.mathsrevision.com Writing Decimals
National 4
NUM 1.2
Writing Decimals
We can take one bit of the chocolate bar
and split it into 10
1st Decimal place
0.01
0.1
2nd Decimal place
19-Apr-17
Created by Mr. Lafferty Maths Dept.

8. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Writing Decimals
Example : Write down the decimal number
represented by the diagram.
(a)
(b)
(c)
(d)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

9. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Writing Decimals
Now try
Exercise 1
Ch3 (page 27)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

10. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
3cm
19-Apr-17
Created by Mr. Lafferty Maths Dept.

11. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Reading Scales
Learning Intention
Success Criteria
1. To explain the steps to read decimal scales.
Understand the steps to work out any decimal scale to 2 decimal places.
2. Solve problems by working out scales.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

12. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Reading Scales
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
0.1
0.0
1.0cm
2.0cm
You must work out what number goes next to each mark
on the scale.
Step 1: Count the number of steps between numbers.
In this case it takes 10 steps to get from 0.0 to 1.0cm.
Step 2: Do the division
“ the difference between numbers”
by the step number
19-Apr-17
Created by Mr. Lafferty Maths Dept.

13. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Reading Scales
Find the values of the arrows 8
9cm
10cm
8.3
8.8
9.5
9.8
Step 1: Count the number of steps between numbers.
In this case it takes 10 steps to get from 8 to 9cm. 10
Step 2: Do the division
“ the difference between numbers”
by the step number
9-8=1
19-Apr-17
Created by Mr. Lafferty Maths Dept.

14. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Reading Harder Scales
3.02
3.04
3.05
3.06
3.07
3.08
3.09
3.11
3.12
3.13
3.14
3.15
3.16
3.17
3.18
3.19
3.01
3.03
3.00cm
3.10cm
3.20cm
You must work out what number goes next to each mark
on the scale.
Step 1: Count the number of steps between numbers.
In this case it takes 10 steps to get from 3.00cm to 3.10cm.
Step 2: Do the division
“ the difference between numbers”
by the step number
19-Apr-17
Created by Mr. Lafferty Maths Dept.

15. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Reading Harder Scales
12.00cm
12.10cm
12.20cm
12.03
12.08
12.14
12.19
Step 1: Count the number of steps between numbers.
In this case it takes 10 steps to get from 12.00cm to 12.10cm.
Step 2: Do the division
“ the difference between numbers”
by the step number
19-Apr-17
Created by Mr. Lafferty Maths Dept.

16. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Reading Scales
Now try Exercise 2
Ch3 (page 29)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

17. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
19-Apr-17
Created by Mr. Lafferty Maths Dept.

18. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Rounding to 1 decimal place
Learning Intention
Success Criteria
To show how to round to 1 decimal place by looking at
the digit at the 2nd decimal place.
1. To be able to round to 1 decimal place.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

19. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Rounding to 1 decimal place
Find the values of the arrows.
8.2cm
8.3cm
8.4cm
8.24
8.28
8.35
Is 8.24 nearer to 8.2 or 8.3 ?
8.2
Is 8.28 nearer to 8.2 or 8.3 ?
8.3
Is 8.35 nearer to 8.2 or 8.3 ?
Neither
19-Apr-17
Created by Mr. Lafferty Maths Dept.

20. Decimal Numbers www.mathsrevision.com Rounding to 1 decimal place
National 4
NUM 1.2
Rounding to 1 decimal place
The rules for rounding to 1 decimal place are:
If the 2nd decimal place is 0,1,2,3,4 - leave 1st decimal place as it is
If the 2nd decimal place is 5,6,7,8,9 - add 1 to 1st decimal place
Example : Round the numbers to 1 decimal place
9.04 (b) (c) 24.25
(d) (e) (f)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

21. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Rounding to 1 decimal place
Now try Exercise 3
Ch3 (page 30)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

22. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
19-Apr-17
Created by Mr. Lafferty Maths Dept.

23. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Add and Subtract Decimals
Learning Intention
Success Criteria
1. Understand that you must keep the decimal point lined up when adding and subtracting decimal numbers.
1. To show how to add and subtract decimal numbers.
2. Show all working.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

24. Decimal Numbers www.mathsrevision.com Add and Subtract Decimals
National 4
NUM 1.2
Add and Subtract Decimals
When you add or subtract decimal numbers,
it is important to line-up the decimal points.
Example 1 : Calculate
19-Apr-17
Created by Mr. Lafferty Maths Dept.

25. Decimal Numbers 3 1 6 www.mathsrevision.com Add and Subtract Decimals
National 4
NUM 1.2
Add and Subtract Decimals
When you add or subtract decimal numbers,
it is important to line-up the decimal points.
Example 1 : Calculate 4 – 0.84 3 1 9 1 3 1 6
19-Apr-17
Created by Mr. Lafferty Maths Dept.

26. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Add and Subtract Decimals
Example 1 : Find the value x cm and y cm
x cm
y cm
3.91cm
2.1cm
y cm
3.25cm
2.2cm
x cm
19-Apr-17
Created by Mr. Lafferty Maths Dept.

27. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Add and Subtract Decimals
Now try Exercise 4
Ch3 (page 32)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

28. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
57o
19-Apr-17
Created by Mr. Lafferty Maths Dept.

29. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiply a decimal by a single digit
Learning Intention
Success Criteria
1. Understand how to multiply and divide a decimal number by a single Digit.
1. To explain how to multiply and divide a decimal number by a single Digit.
2. Show appropriate working.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

30. Decimal Numbers www.mathsrevision.com
National 4
NUM 1.2
Multiply a decimal by a single digit
When multiplying by a single digit
the decimal point always stays in line.
Example : Calculate x 7
19-Apr-17
Created by Mr. Lafferty Maths Dept.

31. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiply a decimal by a single digit
Example : Copy and complete.
3.5 x 6
18.43 x 4
76.97 x 6
19-Apr-17
Created by Mr. Lafferty Maths Dept.

32. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiply a decimal by a single digit
Now try Ex 5
Ch3 (page 34)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

33. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
45o
19-Apr-17
Created by Mr. Lafferty Maths Dept.

34. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Division by a Single Digit
Learning Intention
Success Criteria
1. Understand how to divide a decimal number by a single Digit.
1. To explain how to divide a decimal number by a single Digit.
2. Show appropriate working.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

35. Decimal Numbers www.mathsrevision.com Division by a Single Digit
National 4
NUM 1.2
Division by a Single Digit
When dividing by a single digit
the decimal point always stays in line.
Example : Calculate ÷ 6
19-Apr-17
Created by Mr. Lafferty Maths Dept.

36. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Division by a Single Digit
Example : Copy and complete.
÷ 6
6.52 ÷ 2
95.05 ÷ 5
19-Apr-17
Created by Mr. Lafferty Maths Dept.

37. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Division by a Single Digit
Now try Ex 6
Ch3 (page 35)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

38. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
40o
19-Apr-17
Created by Mr. Lafferty Maths Dept.

39. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiplying & Dividing by 10, 100, 1000
Learning Intention
Success Criteria
1. To understand how to multiply decimal numbers by 10, 100, 1000.
Understand the simple rules to multiply decimal numbers.
2. Be able do calculations.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

40. Decimal Numbers www.mathsrevision.com Multiplying by 10, 100, 1000
National 4
NUM 1.2
Multiplying by 10, 100, 1000
To multiply a decimal number by 10,
Simply move point 1 place to the right:
e.g x 10 = point is moved 1 place to right
To multiply a decimal number by 100,
Simply move point 2 places to the right:
e.g x 100 = point is moved 2 places to right
19-Apr-17
Created by Mr. Lafferty Maths Dept.

41. Decimal Numbers www.mathsrevision.com Multiplying by 10, 100, 1000
National 4
NUM 1.2
Multiplying by 10, 100, 1000
To multiply a decimal number by 1000,
Simply move point 3 places to the right:
e.g x 1000 =
point is moved 3 place to right
19-Apr-17
Created by Mr. Lafferty Maths Dept.

42. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiplying by 10, 100, 1000
Example : Multiply by 10, 100, 1000
10 x =
18.574
100 x =
185.74
1000 x =
1857.4
19-Apr-17
Created by Mr. Lafferty Maths Dept.

43. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiplying & Dividing y 10, 100, 1000
Now try Ex 7
Ch3 (page 37)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

44. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
118o
19-Apr-17
Created by Mr. Lafferty Maths Dept.

45. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiplying & Dividing by 10, 100, 1000
Learning Intention
Success Criteria
1. To understand how to divide decimal numbers by 10, 100, 1000.
Understand the simple rules to divide decimal numbers.
2. Be able do calculations.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

46. Decimal Numbers www.mathsrevision.com Dividing by 10, 100, 1000
National 4
NUM 1.2
Dividing by 10, 100, 1000
To divide a decimal number by 10,
Simply move point 1 place to the left:
e.g. 89 ÷ 10 = 8.9 point is moved 1 place to left
To divide a decimal number by 100,
Simply move point 2 places to the left:
e.g ÷ 100 = point is moved 2 places to left
19-Apr-17
Created by Mr. Lafferty Maths Dept.

47. Decimal Numbers www.mathsrevision.com Dividing by 10, 100, 1000
National 4
NUM 1.2
Dividing by 10, 100, 1000
To divide a decimal number by 1000,
Simply move point 3 places to the left:
e.g ÷ 1000 =
point is moved 3 places to the left
19-Apr-17
Created by Mr. Lafferty Maths Dept.

48. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Dividing by 10, 100, 1000
Example : Divide by 10, 100, 1000
÷ 10 =
4502.4
÷ 100 =
450.24
÷ 1000 =
45.024
19-Apr-17
Created by Mr. Lafferty Maths Dept.

49. Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiplying & Dividing y 10, 100, 1000
Now try Ex 8
Ch3 (page 38)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

50. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
Q1. Solve the equation below
Q2. Find two numbers that multiply to give 18
and subtract to give 3.
Q3. Explain why the average of the numbers below is 7
2,8,8,10
Q4. True or false
19-Apr-17
Created by Mr. Lafferty Maths Dept.

51. Created by Mr. Lafferty Maths Dept.
Units of Length
National 4
NUM 1.2
Learning Intention
Success Criteria
1. To explain the 4 metric units of length and how to convert between them.
To know the 4 units of length.
2. Be able to convert between them.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

52. Created by Mr. Lafferty Maths Dept.
Units of Length
National 4
NUM 1.2
The 4 units of length are :
The metre : This is the standard unit of length and is
approximately the distance from your nose
to the end of your outstretched arm.
100th
The centimetre :
This is of a metre and is about
the width of your pinky nail.
The Millimetre :
This is of a centimetre and is
about the width of a sewing needle.
1000
The Kilometre :
This is metres and is about the
the length of 10 football pitches.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

53. Units of Length Converting Measurements
National 4
NUM 1.2
Kilometres
(km)
metres
(m)
centimetres
(cm)
millimetres
(mm)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

54. Units of Length Converting Measurements
National 4
NUM 1.2
Examples
Convert 2m to cm :
2 x 100 = 200 cm
Convert 4km to m :
4 x 1000 = 4000 m
Convert 34cm to mm :
34 x 10 = 340 mm
Convert 50cm to m :
50 ÷ 100 = 0.5 m
19-Apr-17
Created by Mr. Lafferty Maths Dept.

55. Now try Ch3 (page 8) Extension Booklet Ex9E
Units of Length Converting Measurements
National 4
NUM 1.2
Now try
Extension Booklet Ex9E
Ch3 (page 8)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

56. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
Q1. Solve the equation below
Q2. Find two numbers that multiply to give 14
and subtract to give 5.
Q3. Explain why the average of the numbers below is 9
2,8,8,10,17
Q4. True or false
19-Apr-17
Created by Mr. Lafferty Maths Dept.

57. Created by Mr. Lafferty Maths Dept.
Units of Volume
National 4
NUM 1.2
Learning Intention
Success Criteria
1. To explain the 3 metric units of volume and how to convert between them.
To know the 3 units of volume.
2. Be able to convert between them.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

58. Units of Volume Converting Measurements
1 litre = 1000ml
National 4
NUM 1.2
1 litre = 1000cm3
Litres
(l)
Centilitres
(cl)
Millilitres
(ml)
1 ml = 1cm3
19-Apr-17
Created by Mr. Lafferty Maths Dept.

59. Units of Volume Converting Measurements
National 4
NUM 1.2
Examples
Convert 4 l to cl :
4 x 100 = 400 cl
Convert 500 cl to l :
500 ÷ 100 = 0.5 l
Convert 3 cl to ml :
3 x 10 = 30 ml
Convert 2 l to ml :
2 x 1000 = 2000 ml
19-Apr-17
Created by Mr. Lafferty Maths Dept.

60. Now try Ch3 (page 10) Units of Volume Converting Measurements
National 4
NUM 1.2
Now try
Extension Booklet Ex10E
Ch3 (page 10)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

61. Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
Q1. Solve the equation below
Q2. Find two numbers that multiply to give 2
and subtract to give -1.
Q3. True or false
19-Apr-17
Created by Mr. Lafferty Maths Dept.

62. Created by Mr. Lafferty Maths Dept.
Units of Weight
National 4
NUM 1.2
Learning Intention
Success Criteria
1. To explain the 4 metric units of weight and how to convert between them.
To know the 4 units of weight.
2. Be able to convert between them.
19-Apr-17
Created by Mr. Lafferty Maths Dept.

63. Units of Weight Converting Measurements
National 4
NUM 1.2
Tonnes
(t)
Kilogram
(kg)
Gram
(g)
Milligrams
(mg)
19-Apr-17
Created by Mr. Lafferty Maths Dept.

64. Units of Weight Converting Measurements
National 4
NUM 1.2
Examples
Convert 4 t to kg :
4 x 1000 = 4000 kg
Convert 500 mg to g :
500 ÷ 1000 = 0.5 g
Convert 3 kg to g :
3 x 1000 = 3000 g
Convert g to t :
÷ 1000 ÷ 1000 = 2 t
19-Apr-17
Created by Mr. Lafferty Maths Dept.

65. Now try Ch3 (page 12) Units of Weight Converting Measurements
National 4
NUM 1.2
Now try
Extension Booklet Ex11E
Ch3 (page 12)
19-Apr-17
Created by Mr. Lafferty Maths Dept.