3-aug-15created by mr. lafferty maths dept. working with decimals decimal scales decimal numbers ...

19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.

Working with decimals

Decimal Scales

Decimal Decimal NumbersNumbers

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Multiplying by 10, 100, 1000

Multiplying by a single digit

Rounding to 1 decimal place

Addition and Subtraction

Dividing by 10, 100, 1000

Dividing by a single digit

Converting Volume

Converting Weight

Converting length

National 4 NUM 1.2


Starter QuestionsStarter Questionsw

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1. Find the missing value

2. Calculate of 6000

3. What is the next three numbers in the sequence 9, 15, 21, 27, ...., ...., .... 4. Round 72 to the nearest 10

3 ?=4 20

20%

National 4 NUM 1.2

19 Apr 202319 Apr 2023 Created by Mr. Lafferty Maths Dept.Created by Mr. Lafferty Maths Dept.ww

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1.1. Understand what a decimal Understand what a decimal number is.number is.

1. To explain what a decimal number is. Write down the decimal number represented by a fraction diagram.


2.2. Write down the decimal Write down the decimal number represented by a number represented by a fraction diagram.fraction diagram.

Writing DecimalsNational 4 NUM 1.2


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When you take a When you take a single unitsingle unit and divide it and divide it into 10 bitsinto 10 bits, , what we then have are what we then have are

decimal fractionsdecimal fractions of a whole number of a whole number

Writing Decimals

Imagine, 1 bar of chocolate as our UNIT of measure.

1 (of 1 bar)

10

or 0.1

1

0.110 1. 0

0.1 0.40.2 0.3 0.5

0.6 0.90.7 0.8 1.0

means ten

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Writing Decimals

Example : Write down the decimal number represented by the shaded area.

(a)

(b)

0.3

3 "which means 3 tenths = "

10

0.5

5 1 "which means 5 tenths = = "

10 2

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Writing Decimals

Example : Write down the decimal number represented by the diagram.

(a) (b)

(c) (d)

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We can take one bit of the chocolate bar We can take one bit of the chocolate bar and split it into 10and split it into 10

Writing Decimals

0.10.01

1st Decimal place

2nd Decimal place

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Writing Decimals

Example : Write down the decimal number represented by the diagram.

(a) (b)

(c) (d)

National 4 NUM 1.2


Now try Exercise 1

Ch3 (page 27)

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Writing DecimalsNational 4 NUM 1.2



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2. Calculate 30% of 900

3. Find the area of the rectangle

6cm in length by 4 cm wide.

4. Name the shape.

3cm

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

1. To explain the steps to read decimal scales.


2.2. Solve problems by working Solve problems by working out scales. out scales.

Reading ScalesNational 4 NUM 1.2


You must work out what number goes next to each markon 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

1.0 ÷ 10 = 0.1cm

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0.0 1.0cm 2.0cm

0.10.2

0.30.4

0.50.6

0.70.8

0.9

1.11.2

1.31.4

1.51.6

1.71.8

1.9




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Find the values of the arrows

8.3 8.8 9.5 9.8

8 9cm 10cm


In this case it takes 10 steps to get from 8 to 9cm.



1 ÷ 10 = 0.1cm9-8=1

10




You must work out what number goes next to each markon the scale.


In this case it takes 10 steps to get from 3.00cm to 3.10cm.



0.1 ÷ 10 = 0.01cm

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3.00cm 3.10cm 3.20cm

3.013.02

3.033.04

3.053.06

3.073.08

3.09

3.113.12

3.133.14

3.153.16

3.173.18

3.19


Reading Harder ScalesNational 4 NUM 1.2



In this case it takes 10 steps to get from 12.00cm to 12.10cm.



0.1 ÷ 10 = 0.01cm

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12.00cm 12.10cm 12.20cm


Reading Harder Scales

12.03 12.08 12.14 12.19

National 4 NUM 1.2


Now try Exercise 2Ch3 (page 29)

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o3. I f I am f acing North and turn 90 clockwise, which direction am I f acing

4. How many lines of symmetry has the shape.

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1. To show how to round to 1 decimal place by looking atthe digit at the 2nd decimal place.


1.1. To be able to round to To be able to round to 1 1 decimal place.decimal place.

Rounding to 1 decimal placeNational 4 NUM 1.2


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8.2cm 8.3cm 8.4cm


8.24 8.28 8.35


Find the values of the arrows.

Is 8.24 nearer to 8.2 or 8.3 ? 8.2Is 8.28 nearer to 8.2 or 8.3 ? 8.3Is 8.35 nearer to 8.2 or 8.3 ? Neither

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If the 2nd decimal place is 0,1,2,3,4 - leave 1st decimal place as it is

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

If the 2nd decimal place is 5,6,7,8,9 - add 1 to 1st decimal place

The rules for rounding to 1 decimal place are:

National 4 NUM 1.2



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Rounding to 1 decimal placeNational 4 NUM 1.2



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1. 13 x 7

2. Calculate 23 x 10

3.

4. Find the missing number

3 of 804

1, 1, 2, 3, 5, 8, ...., ...., ....

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1. To show how to add and subtract decimal numbers.

1. Understand that you must keep the decimal point lined up when adding and subtracting decimal numbers.


2. Show all working.

Add and Subtract DecimalsNational 4 NUM 1.2


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Example 1 : Calculate 7.8 + 0.92

When you add or subtract decimal numbers, it is important to line-up the decimal points.

Add and Subtract Decimals

7.80

+0.928 .721

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Example 1 : Calculate 4 – 0.84

When you add or subtract decimal numbers, it is important to line-up the decimal points.


613

4 . 0 0

-0

. 8 4

19 13

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Example 1 : Find the value x cm and y cm


3. 25

-

2.201. 05

2.1cm3.91cm

x cm

2. 10

+ 3.916 .011

x cm y cm

y cm3.25cm

2.2cm

National 4 NUM 1.2



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Add and Subtract DecimalsNational 4 NUM 1.2



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3. Calculate 72 - 58

4. Calculate the value of the missing angle.

57o

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1. To explain how to multiply and divide a decimal number by a single Digit.

1. Understand how to multiply and divide a decimal number by a single Digit.


2. Show appropriate working.

Multiply a decimal by a single digitNational 4 NUM 1.2


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When multiplying by a single digit the decimal point always stays in line.

Example : Calculate 23.68 x 7

2 4 5

23.68

x 7165 .76



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3.5 x 6 18.43 x 4 76.97 x 6




Now try Ex 5Ch3 (page 34)

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3. Calculate 172 - 494. Calculate the value of the missing angle.

45o

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1. To explain how to divide a decimal number by a single Digit.

1. Understand how to divide a decimal number by a single Digit.


2. Show appropriate working.

Division by a Single DigitNational 4 NUM 1.2


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When dividing by a single digit the decimal point always stays in line.

Example : Calculate 17.16 ÷ 6

1 5 3

2 . 8 6 6 17. 16



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Example : Copy and complete.

6.52 ÷ 2 95.05 ÷ 5 204.84 ÷ 6





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1. 46 x 3


3.


35 ?=50 10

1 of 4907

40 o

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1. Understand the simple rules to multiply decimal numbers.

1. To understand how to multiply decimal numbers by 10, 100, 1000.

2. Be able do calculations.


Multiplying & Dividing by 10, 100, 1000National 4 NUM 1.2


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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

Multiplying by 10, 100, 1000

To multiply a decimal number by 100, Simply move point 2 places to the right:

e.g. 1.02 x 100 = 102.0 point is moved 2 places to right

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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 3 place to right

Multiplying by 10, 100, 1000National 4 NUM 1.2


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Example : Multiply 1.8574 by 10, 100, 1000

10 x 1.8574 =

100 x 1.8574 =

1000 x 1.8574 =

18.574

185.74

1857.4

Multiplying by 10, 100, 1000National 4 NUM 1.2



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Multiplying & Dividing y 10, 100, 1000National 4 NUM 1.2



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1. 65 x 30


3.


25 ?=200 8

1 of 632.17

118 o

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1.1. Understand the simple rules Understand the simple rules to divide decimal numbers.to divide decimal numbers.

1. To understand how to divide decimal numbers by 10, 100, 1000.

2.2. Be able do calculations.Be able do calculations.


Multiplying & Dividing by 10, 100, 1000National 4 NUM 1.2


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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

Dividing by 10, 100, 1000

To divide a decimal number by 100, Simply move point 2 places to the left:

e.g. 199 ÷ 100 = 1.99 point is moved 2 places to left

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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

Dividing by 10, 100, 1000National 4 NUM 1.2


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Example : Divide 45 024 by 10, 100, 1000

45 024 ÷ 10 =

45 024 ÷ 100 =

45 024 ÷ 1000 =

4502.4

450.24

45.024

Dividing by 10, 100, 1000National 4 NUM 1.2



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Multiplying & Dividing y 10, 100, 1000National 4 NUM 1.2


Starter Starter QuestionsQuestions

2 16 28 x

60% of £ 240 = £ 144

Q1. Solve the equation below

Q2. Find two numbers that multiply to give 18and subtract to give 3.

Q3. Explain why the average of the numbers below is 7

Q4. True or false

2,8,8,10

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National 4 NUM 1.2


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1.1. To know the 4 units of To know the 4 units of length.length.

1. To explain the 4 metric units of length and how to convert between them. 2. Be able to convert

between them.

Units of LengthUnits of LengthNational 4 NUM 1.2


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Units of LengthUnits of LengthThe 4 units of length are :

The metre : This is the standard unit of length and is approximately the distance from your noseto the end of your outstretched arm.

This is of a metre and is about the width of your pinky nail.

1100

100th

The centimetre :

This is of a centimetre and is aboutthe width of a sewing needle.

110The Millimetre :

This is metres and is about the the length of 10 football pitches.

1000The Kilometre :

1000

National 4 NUM 1.2


Units of Length Units of Length Converting Converting

MeasurementsMeasurements

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(km)

metres(m)

centimetres(cm)

millimetres(mm)

10

100

1000

1000

100

10

National 4 NUM 1.2




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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

National 4 NUM 1.2


Now try Extension Booklet

Ex9E Ch3 (page 8)

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MeasurementsMeasurementsNational 4 NUM 1.2



2 5 11x Q1. Solve the equation below

Q2. Find two numbers that multiply to give 14and subtract to give 5.

Q3. Explain why the average of the numbers below is 9

Q4. True or false

2,8,8,10,17

40% of £ 320 = £ 128

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National 4 NUM 1.2


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1.1. To know the 3 units of To know the 3 units of volume.volume.

1. To explain the 3 metric units of volume and how to convert between them. 2. Be able to convert

between them.

Units of VolumeUnits of VolumeNational 4 NUM 1.2


Units of Volume Converting Units of Volume Converting MeasurementsMeasurements

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Litres(l)

Centilitres(cl)

Millilitres(ml)

10

100

100

10

1 litre = 1000ml

1 litre = 1000cm3

1 ml = 1cm3

National 4 NUM 1.2


Units of Volume Units of Volume Converting Converting


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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

National 4 NUM 1.2


Now try Extension Booklet Ex10E

Ch3 (page 10)

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Units of Volume Units of Volume Converting Converting




4 7 17x Q1. Solve the equation below

Q2. Find two numbers that multiply to give 2and subtract to give -1.

Q3. True or false 20% of £40 = £2

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National 4 NUM 1.2


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1.1. To know the 4 units of To know the 4 units of weight.weight.

1. To explain the 4 metric units of weight and how to convert between them. 2. Be able to convert

between them.

Units of WeightUnits of WeightNational 4 NUM 1.2


Units of Weight Units of Weight Converting Converting


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(t)

Kilogram(kg)

Gram(g)

Milligrams(mg)

1000

1000

1000

1000

1000

1000

National 4 NUM 1.2




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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

National 4 NUM 1.2


Now try Extension Booklet Ex11E

Ch3 (page 12)

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3-aug-15created by mr. lafferty maths dept. working with decimals decimal scales decimal numbers ...

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