Transcript Slide 1
Decimal Numbers www.mathsrevision.com MNU 2-03b MNU 2-04a Working with Decimals Decimal Scales Rounding to 1 Decimal Place Addition and Subtraction Multiplying and Dividing by 10, 100, 1000 Multiplying and Dividing by a single Digit 18-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com MNU 2-03b MNU 2-04a 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 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Writing Decimals www.mathsrevision.com MNU 2-03b MNU 2-04a Learning Intention 1. We are learning what a decimal number is. Write down the decimal number represented by a fraction diagram. 18-Jul-15 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 Writing Decimals www.mathsrevision.com 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 0.1 Imagine, 1 bar of chocolate as our UNIT of 10measure. 1.10 18-Jul-15 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 Writing Decimals MNU 2-03b MNU 2-04a www.mathsrevision.com 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 = 18-Jul-15 Created by Mr. Lafferty Maths Dept. 5 1 = " 10 2 Decimal Numbers Writing Decimals MNU 2-03b MNU 2-04a www.mathsrevision.com Example : Write down the decimal number represented by the diagram. (a) (b) (c) (d) 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Writing Decimals www.mathsrevision.com MNU 2-03b MNU 2-04a We can take one bit of the chocolate bar and split it into 10 1st Decimal place 0.1 0.01 2nd Decimal place 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Writing Decimals MNU 2-03b MNU 2-04a www.mathsrevision.com Example : Write down the decimal number represented by the diagram. (a) (b) (c) (d) 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Writing Decimals www.mathsrevision.com MNU 2-03b MNU 2-04a Now try Exercise 1 Ch2 (page 25) 18-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com MNU 2-03b MNU 2-04a 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. 18-Jul-15 Created by Mr. Lafferty Maths Dept. 3cm Decimal Numbers Reading Scales www.mathsrevision.com MNU 2-03b MNU 2-04a Learning Intention 1 We are learning 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. 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Reading Scales MNU 2-03b MNU 2-04a www.mathsrevision.com 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” 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Reading Scales MNU 2-03b MNU 2-04a www.mathsrevision.com 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 18-Jul-15 Created by Mr. Lafferty Maths Dept. 10 Decimal Numbers Reading Harder Scales MNU 2-03b MNU 2-04a www.mathsrevision.com 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” 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Reading Harder Scales www.mathsrevision.com MNU 2-03b MNU 2-04a 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” 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Reading Scales www.mathsrevision.com MNU 2-03b MNU 2-04a Now try Exercise 2 Ch12 (page 28) 18-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions MNU 2-03b MNU 2-04a www.mathsrevision.com 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. 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Rounding to 1 decimal place www.mathsrevision.com MNU 2-03b MNU 2-04a Learning Intention 1. We are learning how to round to 1 decimal place. 18-Jul-15 Success Criteria 1. Created by Mr. Lafferty Maths Dept. Remember steps to round to 1 decimal place. Decimal Numbers Rounding to 1 decimal place MNU 2-03b MNU 2-04a www.mathsrevision.com 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 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Rounding to 1 decimal place MNU 2-03b MNU 2-04a www.mathsrevision.com 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 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Rounding to 1 decimal place www.mathsrevision.com MNU 2-03b MNU 2-04a Now try Exercise 3 Ch2 (page 30) 18-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions MNU 2-03b MNU 2-04a www.mathsrevision.com 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, ...., ...., .... 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Add and Subtract Decimals www.mathsrevision.com MNU 2-03b MNU 2-04a Learning Intention 1. We are learning 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. 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Add and Subtract Decimals www.mathsrevision.com 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 7.80 +0.92 8 .72 1 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Add and Subtract Decimals www.mathsrevision.com 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 3 4 .9010 -0.84 3.1 6 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Add and Subtract Decimals www.mathsrevision.com MNU 2-03b MNU 2-04a 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 18-Jul-15 3.91cm 3.25cm Created by Mr. Lafferty Maths Dept. y cm 2.1cm 2.2cm x cm Decimal Numbers Add and Subtract Decimals www.mathsrevision.com MNU 2-03b MNU 2-04a Now try Exercise 4 Ch2 (page 32) 18-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions MNU 2-03b MNU 2-04a www.mathsrevision.com 1. 46 x 3 35 ? 2. Find the missing value = 50 10 1 3. of 490 7 4. Calculate the value of the missing angle. 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Multiplying & Dividing by 10, 100, 1000 www.mathsrevision.com MNU 2-03b MNU 2-04a Learning Intention 1 We are learning how to multiply and divide decimal numbers by 10, 100, 1000. Success Criteria 1. Understand the simple rules to multiply and divide decimal numbers. 2. Be able do calculations. 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Multiplying by 10, 100, 1000 www.mathsrevision.com 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: e.g. 18-Jul-15 1.02 x 100 = 102.0 point is moved 2 places to right Created by Mr. Lafferty Maths Dept. Decimal Numbers Multiplying by 10, 100, 1000 www.mathsrevision.com MNU 2-03b MNU 2-04a To multiply a decimal number by 1000, Simply move point 3 places to the right: e.g. 18-Jul-15 34.567 x 1000 = 34 567 point is moved 1 place to right Created by Mr. Lafferty Maths Dept. Decimal Numbers Multiplying by 10, 100, 1000 MNU 2-03b MNU 2-04a www.mathsrevision.com 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 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Multiplying & Dividing y 10, 100, 1000 www.mathsrevision.com MNU 2-03b MNU 2-04a Now try Ex 5 First Column in each Question ONLY Ch2 (page 35) 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Dividing by 10, 100, 1000 www.mathsrevision.com 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: e.g. 18-Jul-15 199 ÷ 100 = 1.99 point is moved 2 places to left Created by Mr. Lafferty Maths Dept. Decimal Numbers Dividing by 10, 100, 1000 www.mathsrevision.com MNU 2-03b MNU 2-04a To divide a decimal number by 1000, Simply move point 3 places to the left: e.g. 18-Jul-15 35 837 ÷ 1000 = 35.837 point is moved 3 places to the left Created by Mr. Lafferty Maths Dept. Decimal Numbers Dividing by 10, 100, 1000 MNU 2-03b MNU 2-04a www.mathsrevision.com Example : Divide 45 024 by 10, 100, 1000 45 024 ÷ 10 = 4502.4 45 024 ÷ 100 = 450.24 45 024 ÷ 1000 = 45.024 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers Multiplying & Dividing y 10, 100, 1000 www.mathsrevision.com MNU 2-03b MNU 2-04a Now try Ex 6 First Column in each Question ONLY Ch2 (page 35) 18-Jul-15 Created by Mr. Lafferty Maths Dept. Starter Questions www.mathsrevision.com MNU 2-03b MNU 2-04a 1. 320 8 2. Calculate 20% of 360 3. Calculate 72 - 58 4. Calculate the value of the missing angle. 18-Jul-15 Created by Mr. Lafferty Maths Dept. 57o Decimal Numbers www.mathsrevision.com MNU 2-03b MNU 2-04a Multiplication & Division by a Single Digit Learning Intention 1. We are learning 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. 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers www.mathsrevision.com MNU 2-03b MNU 2-04a Multiplication & Division 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 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers www.mathsrevision.com MNU 2-03b MNU 2-04a Multiplication & 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 18-Jul-15 Created by Mr. Lafferty Maths Dept. Decimal Numbers www.mathsrevision.com MNU 2-03b MNU 2-04a Multiplication & Division by a Single Digit Example : Copy and complete. 3.5 x 6 6.52 ÷ 2 18-Jul-15 18.43 x 4 95.05 ÷ 5 Created by Mr. Lafferty Maths Dept. 76.97 x 6 204.84 ÷ 6 Decimal Numbers www.mathsrevision.com MNU 2-03b MNU 2-04a Multiplication & Division by a Single Digit Now try Ex 7 & 8 Ch2 (page 37) 18-Jul-15 Created by Mr. Lafferty Maths Dept.