Transcript Decimal Numbers - Mathsrevision.com

Decimal Numbers
National 4
NUM 1.2
Working with decimals
www.mathsrevision.com
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
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
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National 4
NUM 1.2
1. Find the missing value
3 ?
=
4 20
2. Calculate 20% of 6000
3. What is the next three numbers
in the sequence
9, 15, 21, 27, ...., ...., ....
4. Round 72 to the nearest 10
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Writing Decimals
Learning Intention
1.
11-Apr-17
To explain what a decimal
number is. Write down the
decimal number
represented by a fraction
diagram.
Success Criteria
1. Understand what a decimal
number is.
2. Write down the decimal
number represented by a
fraction diagram.
Created by Mr. Lafferty Maths Dept.
means ten
Decimal Numbers
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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
0.1
Imagine, 1 bar of chocolate as our UNIT of
10measure.
1.10
11-Apr-17
0.1 0.2 0.3 0.4 0.5
1
(of 1 bar)
10
0.6 0.7 0.8 0.9 1.0
or 0.1
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Writing Decimals
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Example :
Write down the decimal number
represented by the shaded area.
(a)
0.3
3
"which means 3 tenths = "
10
(b)
0.5
"which means 5 tenths =
11-Apr-17
Created by Mr. Lafferty Maths Dept.
5 1
= "
10 2
Decimal Numbers
National 4
NUM 1.2
Writing Decimals
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Example :
Write down the decimal number
represented by the diagram.
(a)
(b)
(c)
(d)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Writing Decimals
We can take one bit of the chocolate bar
and split it into 10
1st Decimal place
0.1
0.01
2nd Decimal place
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Writing Decimals
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Example :
Write down the decimal number
represented by the diagram.
(a)
(b)
(c)
(d)
11-Apr-17
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Decimal Numbers
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National 4
NUM 1.2
Writing Decimals
Now try
Exercise 1
Ch3 (page 27)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
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National 4
NUM 1.2
1. Find the perimeter of the shape
2. Calculate 30% of 900
3. Find the area of the rectangle
6cm in length by 4 cm wide.
4. Name the shape.
11-Apr-17
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3cm
Decimal Numbers
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National 4
NUM 1.2
Reading Scales
Learning Intention
1.
To explain the steps to
read decimal scales.
Success Criteria
1. Understand the steps to work
out any decimal scale to 2
decimal places.
2. Solve problems by working out
scales.
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Decimal Numbers
National 4
NUM 1.2
Reading Scales
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0.2 0.4
0.6
0.8
0.1
0.3
0.5
0.7
0.9
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
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.
In this case it takes 10 steps to get from 0.0 to 1.0cm.
Step 2: Do the division
by the step number
1.0 ÷ 10 = 0.1cm
“ the difference between numbers”
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Reading Scales
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Find the values of the arrows
9cm
8
8.3
8.8
10cm
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.
Step 2: Do the division
by the step number
1 ÷ 10 = 0.1cm
“ the difference between numbers”
9-8=1
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Created by Mr. Lafferty Maths Dept.
10
Decimal Numbers
National 4
NUM 1.2
Reading Harder Scales
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3.12 3.14 3.16 3.18
3.02 3.04 3.06 3.08
3.01 3.03 3.05 3.07 3.09 3.11 3.13 3.15 3.17 3.19
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.
In this case it takes 10 steps to get from 3.00cm to 3.10cm.
Step 2: Do the division
by the step number
0.1 ÷ 10 = 0.01cm
“ the difference between numbers”
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Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Reading Harder Scales
12.10cm
12.00cm
12.08
12.03
12.20cm
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
by the step number
0.1 ÷ 10 = 0.01cm
“ the difference between numbers”
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Decimal Numbers
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National 4
NUM 1.2
Reading Scales
Now try Exercise 2
Ch3 (page 29)
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Starter Questions
National 4
NUM 1.2
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1. Name the part of the circle.
2. Calculate 60% of 300
3. If I am facing North and turn 90o
clockwise, which direction am I facing
4. How many lines of symmetry
has the shape.
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Decimal Numbers
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National 4
NUM 1.2
Rounding to 1 decimal place
Learning Intention
1. To show how to round to 1
decimal place by looking at
the digit at the 2nd decimal
place.
11-Apr-17
Success Criteria
1.
Created by Mr. Lafferty Maths Dept.
To be able to round to 1
decimal place.
Decimal Numbers
National 4
NUM 1.2
Rounding to 1 decimal place
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Find the values of the arrows.
8.3cm
8.2cm
8.24
8.4cm
8.35
8.28
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
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Decimal Numbers
National 4
NUM 1.2
Rounding to 1 decimal place
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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
(a)
9.04
(b)
18.08
(c)
24.25
(d)
12.73
(e)
102.09
(f)
2636.55
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Rounding to 1 decimal place
Now try Exercise 3
Ch3 (page 30)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
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1.
13 x 7
2. Calculate 23 x 10
3
3.
of 80
4
4. Find the missing number
1, 1, 2, 3, 5, 8, ...., ...., ....
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Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Add and Subtract Decimals
Learning Intention
1. To show how to add and
subtract decimal numbers.
Success Criteria
1. Understand that you must
keep the decimal point
lined up when adding and
subtracting decimal
numbers.
2. Show all working.
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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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 7.8 + 0.92
7.80
+0.92
8 .72
1
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Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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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
9 1
1
4.00
-0 . 8 4
3 16
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Add and Subtract Decimals
Example 1 : Find the value x cm and y cm
x cm
y cm
2. 10
3. 25
+ 3.91
6 .01
1
- 2.20
1. 05
11-Apr-17
3.91cm
3.25cm
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y cm
2.1cm
2.2cm
x cm
Decimal Numbers
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National 4
NUM 1.2
Add and Subtract Decimals
Now try Exercise 4
Ch3 (page 32)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
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National 4
NUM 1.2
1. 320  8
2. Calculate 20% of 360
3. Calculate 72 - 58
4. Calculate the value of the
missing angle.
11-Apr-17
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57o
Decimal Numbers
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National 4
NUM 1.2
Multiply a decimal by a single digit
Learning Intention
1. To explain how to multiply
and divide a decimal
number by a single Digit.
Success Criteria
1. Understand how to
multiply and divide a
decimal number by a single
Digit.
2. Show appropriate working.
11-Apr-17
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Decimal Numbers
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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 23.68 x 7
23.68
x7
165 .76
2 4 5
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Decimal Numbers
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National 4
NUM 1.2
Multiply a decimal by a single digit
Example :
3.5 x 6
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Copy and complete.
18.43 x 4
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76.97 x 6
Decimal Numbers
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National 4
NUM 1.2
Multiply a decimal by a single digit
Now try Ex 5
Ch3 (page 34)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
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National 4
NUM 1.2
1. 400  80
2. Calculate 30% of 360
3. Calculate 172 - 49
4. Calculate the value of the
missing angle.
11-Apr-17
Created by Mr. Lafferty Maths Dept.
45o
Decimal Numbers
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National 4
NUM 1.2
Division by a Single Digit
Learning Intention
1. To explain how to divide a
decimal number by a single
Digit.
Success Criteria
1. Understand how to divide
a decimal number by a
single Digit.
2. Show appropriate working.
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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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 17.16 ÷ 6
2.86
1 5 3
6 1 7. 1 6
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Decimal Numbers
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National 4
NUM 1.2
Division by a Single Digit
Example :
6.52 ÷ 2
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Copy and complete.
95.05 ÷ 5
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204.84 ÷ 6
Decimal Numbers
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National 4
NUM 1.2
Division by a Single Digit
Now try Ex 6
Ch3 (page 35)
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Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
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1. 46 x 3
2. Find the missing value
35 ?
=
50 10
1
3.
of 490
7
4. Calculate the value of the
missing angle.
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Multiplying & Dividing by 10, 100, 1000
Learning Intention
1.
To understand how to
multiply decimal numbers
by 10, 100, 1000.
Success Criteria
1. Understand the simple rules
to multiply decimal numbers.
2. Be able do calculations.
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
www.mathsrevision.com
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.
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:
e.g.
11-Apr-17
1.02 x 100 = 102.0 point is moved 2 places to right
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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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.
11-Apr-17
34.567 x 1000 = 34 567
point is moved 3 place to right
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Multiplying by 10, 100, 1000
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Example : Multiply 1.8574 by 10, 100, 1000
10 x 1.8574 = 18.574
100 x 1.8574 = 185.74
1000 x 1.8574 = 1857.4
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Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Multiplying & Dividing y 10, 100, 1000
Now try Ex 7
Ch3 (page 37)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
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1. 65 x 30
2. Find the missing value
25 ?
=
200 8
1
3.
of 632.1
7
4. Calculate the value of the
missing angle.
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
www.mathsrevision.com
National 4
NUM 1.2
Multiplying & Dividing by 10, 100, 1000
Learning Intention
1.
To understand how to
divide decimal numbers by
10, 100, 1000.
Success Criteria
1. Understand the simple rules
to divide decimal numbers.
2. Be able do calculations.
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
www.mathsrevision.com
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.
11-Apr-17
199 ÷ 100 = 1.99
point is moved 2 places to left
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
www.mathsrevision.com
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.
11-Apr-17
35 837 ÷ 1000 = 35.837
point is moved 3 places to the left
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
National 4
NUM 1.2
Dividing by 10, 100, 1000
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Example : Divide 45 024 by 10, 100, 1000
45 024 ÷ 10 = 4502.4
45 024 ÷ 100 = 450.24
45 024 ÷ 1000 = 45.024
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Decimal Numbers
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National 4
NUM 1.2
Multiplying & Dividing y 10, 100, 1000
Now try Ex 8
Ch3 (page 38)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
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Q1.
Solve the equation below
2x  16  28
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.
11-Apr-17
True or false
60% of £240 = £144
Created by Mr. Lafferty Maths Dept.
Units of Length
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National 4
NUM 1.2
Learning Intention
1.
11-Apr-17
Success Criteria
To explain the 4 metric
units of length and how to
convert between them.
1. To know the 4 units of
length.
2. Be able to convert
between them.
Created by Mr. Lafferty Maths Dept.
Units of Length
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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
th
100
to the end of your outstretched arm.
1
100
The centimetre :
This is
of a metre and is about
the width of your pinky nail.
The Millimetre :
1000
This is 10 of a centimetre and is
about the width of a sewing needle.
The Kilometre :
11-Apr-17
1
This is 1000 metres and is about the
the length of 10 football pitches.
Created by Mr. Lafferty Maths Dept.
Units of Length
Converting Measurements
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National 4
NUM 1.2
1000
Kilometres
(km)
100
metres
(m)
1000
100
centimetres
(cm)
10
11-Apr-17
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10
millimetres
(mm)
National 4
NUM 1.2
Units of Length
Converting Measurements
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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 :
11-Apr-17
50 ÷ 100 = 0.5 m
Created by Mr. Lafferty Maths Dept.
Units of Length
Converting Measurements
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National 4
NUM 1.2
Now try
Extension Booklet Ex9E
Ch3 (page 8)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
National 4
NUM 1.2
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Q1.
Solve the equation below
2x  5  11
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.
11-Apr-17
True or false 40% of £320 = £128
Created by Mr. Lafferty Maths Dept.
Units of Volume
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National 4
NUM 1.2
Learning Intention
1.
11-Apr-17
To explain the 3 metric
units of volume and how to
convert between them.
Success Criteria
1. To know the 3 units of
volume.
2. Be able to convert
between them.
Created by Mr. Lafferty Maths Dept.
1 litre = 1000ml
Units of Volume Converting
Measurements
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National 4
NUM 1.2
100
Litres
(l)
1 litre = 1000cm3
10
Centilitres
(cl)
100
10
11-Apr-17
Millilitres
(ml)
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1 ml = 1cm3
National 4
NUM 1.2
Units of Volume
Converting Measurements
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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
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Units of Volume
Converting Measurements
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National 4
NUM 1.2
Now try
Extension Booklet Ex10E
Ch3 (page 10)
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Starter Questions
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National 4
NUM 1.2
Q1.
Solve the equation below
Q2.
4x  7  17
Find two numbers that multiply to give 2
and subtract to give -1.
Q3.
True or false
11-Apr-17
20% of £40 = £2
Created by Mr. Lafferty Maths Dept.
Units of Weight
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National 4
NUM 1.2
Learning Intention
1.
11-Apr-17
To explain the 4 metric
units of weight and how to
convert between them.
Success Criteria
1. To know the 4 units of
weight.
2. Be able to convert
between them.
Created by Mr. Lafferty Maths Dept.
Units of Weight
Converting Measurements
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National 4
NUM 1.2
1000
Tonnes
(t)
1000
Kilogram
(kg)
1000
Gram
(g)
1000
1000
11-Apr-17
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1000
Milligrams
(mg)
National 4
NUM 1.2
Units of Weight
Converting Measurements
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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 2000000 g to t : 2000000 ÷ 1000 ÷ 1000 = 2 t
11-Apr-17
Created by Mr. Lafferty Maths Dept.
Units of Weight
Converting Measurements
www.mathsrevision.com
National 4
NUM 1.2
Now try
Extension Booklet Ex11E
Ch3 (page 12)
11-Apr-17
Created by Mr. Lafferty Maths Dept.