Decimal Numbers

1
Decimal Numbers
MNU 2-03b MNU 2-04a
Working with Decimals
Decimal Scales
Rounding to 1 Decimal Place

www.mathsrevision.com
Addition and Subtraction

Multiplying and Dividing by 10, 100, 1000
Multiplying and Dividing by a single Digit
2
Starter Questions
MNU 2-03b MNU 2-04a
www.mathsrevision.com
3
Decimal Numbers
Writing Decimals
MNU 2-03b MNU 2-04a
Learning Intention
Success Criteria

1. Understand what a decimal number is.

1. We are learning what a decimal number is.
Write down the decimal number represented by a
fraction diagram.
2. Write down the decimal number represented by a
fraction diagram.
www.mathsrevision.com
4
means ten
Decimal Numbers
Writing Decimals
MNU 2-03b MNU 2-04a
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.
www.mathsrevision.com
0.1
0.4
0.2
0.3
0.5
0.6
0.9
0.7
0.8
1.0
or 0.1
5
Decimal Numbers
Writing Decimals
MNU 2-03b MNU 2-04a
Example Write down the decimal number
represented by the shaded area.
(a)
www.mathsrevision.com
(b)
6
Decimal Numbers
Writing Decimals
MNU 2-03b MNU 2-04a
Example Write down the decimal number
represented by the diagram.
(a)
(b)
www.mathsrevision.com
(c)
(d)
7
Decimal Numbers
Writing Decimals
MNU 2-03b MNU 2-04a
We can take one bit of the chocolate bar and
split it into 10
1st Decimal place
0.01
0.1
www.mathsrevision.com
2nd Decimal place
8
Decimal Numbers
Writing Decimals
MNU 2-03b MNU 2-04a
Example Write down the decimal number
represented by the diagram.
(a)
(b)
www.mathsrevision.com
(c)
(d)
9
Decimal Numbers
Writing Decimals
MNU 2-03b MNU 2-04a
Now try Exercise 1 Ch2 (page 25)
www.mathsrevision.com
10
Starter Questions
MNU 2-03b MNU 2-04a
3cm
www.mathsrevision.com
11
Decimal Numbers
Reading Scales
MNU 2-03b MNU 2-04a
Learning Intention
Success Criteria

1. Understand the steps to work out any decimal
   scale to 2 decimal places.

1 We are learning the steps to read decimal
scales.
2. Solve problems by working out scales.
www.mathsrevision.com
12
Decimal Numbers
Reading Scales
MNU 2-03b MNU 2-04a
0.2
0.1
1.0cm
0.0
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.
www.mathsrevision.com
In this case it takes 10 steps to get from 0.0 to
1.0cm.
Step 2 Do the division
by the step number
the difference between numbers
13
Decimal Numbers
Reading Scales
MNU 2-03b MNU 2-04a
Find the values of the arrows
9cm
8
10cm
8.8
9.5
9.8
8.3
Step 1 Count the number of steps between numbers.
www.mathsrevision.com
In this case it takes 10 steps to get from 8 to
9cm.
10
Step 2 Do the division
by the step number
the difference between numbers
9-81
14

Decimal Numbers
Reading Harder Scales
MNU 2-03b MNU 2-04a
3.02
3.01
3.03
3.10cm
3.00cm
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.
www.mathsrevision.com
In this case it takes 10 steps to get from 3.00cm
to 3.10cm.
Step 2 Do the division
by the step number
the difference between numbers
15

Decimal Numbers
Reading Harder Scales
MNU 2-03b MNU 2-04a
12.10cm
12.00cm
12.20cm
12.19
12.14
12.08
12.03
Step 1 Count the number of steps between numbers.
www.mathsrevision.com
In this case it takes 10 steps to get from
12.00cm to 12.10cm.
Step 2 Do the division
by the step number
the difference between numbers
16
Decimal Numbers
Reading Scales
MNU 2-03b MNU 2-04a
Now try Exercise 2 Ch12 (page 28)
www.mathsrevision.com
17
Starter Questions
MNU 2-03b MNU 2-04a
www.mathsrevision.com
18
Decimal Numbers
Rounding to 1 decimal place
MNU 2-03b MNU 2-04a
Learning Intention
Success Criteria

1. We are learning how to round to 1 decimal place.

1. Remember steps to round to 1 decimal place.
www.mathsrevision.com
19

Decimal Numbers
Rounding to 1 decimal place
MNU 2-03b MNU 2-04a
Find the values of the arrows.
8.3cm
8.2cm
8.4cm
8.24
8.35
8.28
www.mathsrevision.com
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
20
Decimal Numbers
Rounding to 1 decimal place
MNU 2-03b MNU 2-04a
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
www.mathsrevision.com
21
Decimal Numbers
Rounding to 1 decimal place
MNU 2-03b MNU 2-04a
Now try Exercise 3 Ch2 (page 30)
www.mathsrevision.com
22
Starter Questions
MNU 2-03b MNU 2-04a
www.mathsrevision.com
23
Decimal Numbers
Add and Subtract Decimals
MNU 2-03b MNU 2-04a
Learning Intention
Success Criteria
1. Understand that you must keep the decimal
point lined up when adding and subtracting
decimal numbers.
1. We are learning how to add and subtract
decimal numbers.
www.mathsrevision.com
2. Show all working.
24
Decimal Numbers
Add and Subtract Decimals
MNU 2-03b MNU 2-04a
When you add or subtract decimal numbers, it is
important to line-up the decimal points.
Example 1 Calculate 7.8 0.92
www.mathsrevision.com
25
Decimal Numbers
Add and Subtract Decimals
MNU 2-03b MNU 2-04a
When you add or subtract decimal numbers, it is
important to line-up the decimal points.
Example 1 Calculate 4 0.84
www.mathsrevision.com
26
Decimal Numbers
Add and Subtract Decimals
MNU 2-03b MNU 2-04a
Example 1 Find the value x cm and y cm
x cm
y cm
3.91cm
2.1cm
y cm
3.25cm
www.mathsrevision.com
2.2cm
x cm
27
Decimal Numbers
Add and Subtract Decimals
MNU 2-03b MNU 2-04a
Now try Exercise 4 Ch2 (page 32)
www.mathsrevision.com
28
Starter Questions
MNU 2-03b MNU 2-04a
www.mathsrevision.com
29
Decimal Numbers
Multiplying Dividing by 10, 100, 1000
MNU 2-03b MNU 2-04a
Learning Intention
Success Criteria

1. Understand the simple rules to multiply and
   divide decimal numbers.

1 We are learning how to multiply and divide
decimal numbers by 10, 100, 1000.
www.mathsrevision.com
2. Be able do calculations.
30
Decimal Numbers
Multiplying by 10, 100, 1000
MNU 2-03b MNU 2-04a
To multiply a decimal number by 10, Simply move
point 1 place to the right
e.g. 2.55 x 10 25.5 point is moved 1 place to
right
To multiply a decimal number by 100, Simply move
point 2 places to the right
www.mathsrevision.com
e.g. 1.02 x 100 102.0 point is moved 2 places
to right
31
Decimal Numbers
Multiplying by 10, 100, 1000
MNU 2-03b MNU 2-04a
To multiply a decimal number by 1000, Simply
move point 3 places to the right
e.g. 34.567 x 1000 34 567 point is moved 1
place to right
www.mathsrevision.com
32
Decimal Numbers
Multiplying by 10, 100, 1000
MNU 2-03b MNU 2-04a
Example Multiply 1.8574 by 10, 100, 1000
10 x 1.8574
18.574
100 x 1.8574
185.74
www.mathsrevision.com
1000 x 1.8574
1857.4
33
Decimal Numbers
Multiplying Dividing y 10, 100, 1000
MNU 2-03b MNU 2-04a
Now try Ex 5 First Column in each Question
ONLY Ch2 (page 35)
www.mathsrevision.com
34
Decimal Numbers
Dividing by 10, 100, 1000
MNU 2-03b MNU 2-04a
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
www.mathsrevision.com
e.g. 199 100 1.99 point is moved 2 places
to left
35
Decimal Numbers
Dividing by 10, 100, 1000
MNU 2-03b MNU 2-04a
To divide a decimal number by 1000, Simply move
point 3 places to the left
e.g. 35 837 1000 35.837 point is moved 3
places to the left
www.mathsrevision.com
36
Decimal Numbers
Dividing by 10, 100, 1000
MNU 2-03b MNU 2-04a
Example Divide 45 024 by 10, 100, 1000
45 024 10
4502.4
45 024 100
450.24
www.mathsrevision.com
45 024 1000
45.024
37
Decimal Numbers
Multiplying Dividing y 10, 100, 1000
MNU 2-03b MNU 2-04a
Now try Ex 6 First Column in each Question
ONLY Ch2 (page 35)
www.mathsrevision.com
38
Starter Questions
MNU 2-03b MNU 2-04a
www.mathsrevision.com
57o
39
Decimal Numbers
Multiplication Division by a Single Digit
MNU 2-03b MNU 2-04a
Learning Intention
Success Criteria
1. Understand how to multiply and divide a
decimal number by a single Digit.
1. We are learning how to multiply and divide a
decimal number by a single Digit.
www.mathsrevision.com
2. Show appropriate working.
40
Decimal Numbers
Multiplication Division by a Single Digit
MNU 2-03b MNU 2-04a
When multiplying by a single digit the decimal
point always stays in line.
Example Calculate 23.68 x 7
www.mathsrevision.com
41
Decimal Numbers
Multiplication Division by a Single Digit
MNU 2-03b MNU 2-04a
When dividing by a single digit the decimal
point always stays in line.
Example Calculate 17.16 6
www.mathsrevision.com
42
Decimal Numbers
Multiplication Division by a Single Digit
MNU 2-03b MNU 2-04a
Example Copy and complete.
3.5 x 6
18.43 x 4
76.97 x 6
www.mathsrevision.com
204.84 6
6.52 2
95.05 5
43
Decimal Numbers
Multiplication Division by a Single Digit
MNU 2-03b MNU 2-04a
Now try Ex 7 8 Ch2 (page 37)
www.mathsrevision.com