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 www.mathsrevision.com 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.

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

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. www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. www.mathsrevision.com 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.

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) www.mathsrevision.com (b) 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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) www.mathsrevision.com (c) (d) 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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 www.mathsrevision.com 2nd Decimal place 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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) www.mathsrevision.com (c) (d) 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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

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

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. www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. www.mathsrevision.com 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.

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. www.mathsrevision.com 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.

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. www.mathsrevision.com 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.

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. www.mathsrevision.com 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.

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

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

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. www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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 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 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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) 18.08 (c) 24.25 (d) 12.73 (e) 102.09 (f) 2636.55 www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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) www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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

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. www.mathsrevision.com 2. Show all working. 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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 7.8 + 0.92 www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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 www.mathsrevision.com 3 1 9 1 3 1 6 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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 www.mathsrevision.com 2.2cm x cm 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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

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

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. www.mathsrevision.com 2. Show appropriate working. 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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 23.68 x 7 www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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 www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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) www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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

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. www.mathsrevision.com 2. Show appropriate working. 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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 17.16 ÷ 6 www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Decimal Numbers National 4 NUM 1.2 Division by a Single Digit Example : Copy and complete. 204.84 ÷ 6 6.52 ÷ 2 95.05 ÷ 5 www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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) www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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

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. www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. 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 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. 34.567 x 1000 = 34 567 point is moved 3 place to right www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Decimal Numbers National 4 NUM 1.2 Multiplying by 10, 100, 1000 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 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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) www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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

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. www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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: www.mathsrevision.com e.g. 199 ÷ 100 = 1.99 point is moved 2 places to left 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. 35 837 ÷ 1000 = 35.837 point is moved 3 places to the left www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

Created by Mr. Lafferty Maths Dept. Decimal Numbers National 4 NUM 1.2 Dividing by 10, 100, 1000 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 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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) www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. www.mathsrevision.com 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.

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. www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. www.mathsrevision.com 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.

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

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 www.mathsrevision.com 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.

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) www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. www.mathsrevision.com 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.

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. www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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

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 www.mathsrevision.com 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.

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

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. www.mathsrevision.com Q3. True or false 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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. www.mathsrevision.com 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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

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 www.mathsrevision.com Convert 3 kg to g : 3 x 1000 = 3000 g Convert 2000000 g to t : 2000000 ÷ 1000 ÷ 1000 = 2 t 19-Apr-17 Created by Mr. Lafferty Maths Dept.

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