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Decimal Numbers

National 4 NUM 1.2. Working with decimals. Decimal Numbers. 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.

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Decimal Numbers

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  1. National 4 NUM 1.2 Working with decimals Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  2. National 4 NUM 1.2 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  3. Decimal Numbers National 4 NUM 1.2 Writing Decimals Learning Intention Success Criteria • Understand what a decimal number is. • 1. To explain 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 Created by Mr. Lafferty Maths Dept.

  4. means ten Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  5. 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) Created by Mr. Lafferty Maths Dept.

  6. 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) Created by Mr. Lafferty Maths Dept.

  7. Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  8. 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) Created by Mr. Lafferty Maths Dept.

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

  10. National 4 NUM 1.2 Starter Questions 3cm www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  11. Decimal Numbers National 4 NUM 1.2 Reading Scales Learning Intention Success Criteria • Understand the steps to work out any decimal scale to 2 decimal places. • 1. To explain the steps to read decimal scales. • 2. Solve problems by working out scales. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  12. 0.4 0.6 0.8 1.2 1.4 1.6 1.8 0.3 0.5 0.7 0.9 1.1 1.3 1.5 1.7 1.9 Decimal Numbers National 4 NUM 1.2 Reading Scales 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” Created by Mr. Lafferty Maths Dept.

  13. Decimal Numbers National 4 NUM 1.2 Reading Scales 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” 9-8=1 Created by Mr. Lafferty Maths Dept.

  14. 3.12 3.14 3.04 3.16 3.06 3.18 3.08 3.11 3.13 3.05 3.15 3.17 3.07 3.19 3.09 Decimal Numbers National 4 NUM 1.2 Reading Harder Scales 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” Created by Mr. Lafferty Maths Dept.

  15. Decimal Numbers National 4 NUM 1.2 Reading Harder Scales 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” Created by Mr. Lafferty Maths Dept.

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

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

  18. Decimal Numbers National 4 NUM 1.2 Rounding to 1 decimal place Learning Intention Success Criteria • 1. To be able to round to 1 decimal place. • To show how to round to 1 decimal place by looking at • the digit at the 2nd decimal place. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  19. Decimal Numbers National 4 NUM 1.2 Rounding to 1 decimal place Find the values of the arrows. 8.3cm 8.2cm 8.4cm 8.35 8.24 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 Created by Mr. Lafferty Maths Dept.

  20. 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 Decimal Numbers 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 www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  21. Decimal Numbers National 4 NUM 1.2 Rounding to 1 decimal place Now try Exercise 3 Ch3 (page 30) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  22. National 4 NUM 1.2 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  23. 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. Created by Mr. Lafferty Maths Dept.

  24. Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  25. Decimal Numbers 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 9 3 1 1 3 1 6 Created by Mr. Lafferty Maths Dept.

  26. 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 Created by Mr. Lafferty Maths Dept.

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

  28. National 4 NUM 1.2 Starter Questions www.mathsrevision.com 57o Created by Mr. Lafferty Maths Dept.

  29. 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. Created by Mr. Lafferty Maths Dept.

  30. Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  31. 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 Created by Mr. Lafferty Maths Dept.

  32. Decimal Numbers National 4 NUM 1.2 Multiply a decimal by a single digit Now try Ex 5 Ch3 (page 34) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  33. National 4 NUM 1.2 Starter Questions www.mathsrevision.com 45o Created by Mr. Lafferty Maths Dept.

  34. 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. Created by Mr. Lafferty Maths Dept.

  35. Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  36. 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 Created by Mr. Lafferty Maths Dept.

  37. Decimal Numbers National 4 NUM 1.2 Division by a Single Digit Now try Ex 6 Ch3 (page 35) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  38. 40o National 4 NUM 1.2 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  39. Decimal Numbers National 4 NUM 1.2 Multiplying & Dividing by 10, 100, 1000 Learning Intention Success Criteria • 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. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  40. Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  41. Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  42. 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 Created by Mr. Lafferty Maths Dept.

  43. Decimal Numbers National 4 NUM 1.2 Multiplying & Dividing y 10, 100, 1000 Now try Ex 7 Ch3 (page 37) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  44. 118o National 4 NUM 1.2 Starter Questions www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  45. Decimal Numbers National 4 NUM 1.2 Multiplying & Dividing by 10, 100, 1000 Learning Intention Success Criteria • Understand the simple rules to divide decimal numbers. • 1. To understand how to divide decimal numbers by 10, 100, 1000. • 2. Be able do calculations. www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  46. Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  47. Decimal Numbers 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 Created by Mr. Lafferty Maths Dept.

  48. 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 Created by Mr. Lafferty Maths Dept.

  49. Decimal Numbers National 4 NUM 1.2 Multiplying & Dividing y 10, 100, 1000 Now try Ex 8 Ch3 (page 38) www.mathsrevision.com Created by Mr. Lafferty Maths Dept.

  50. 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. Q3. Explain why the average of the numbers below is 7 www.mathsrevision.com 2,8,8,10 Q4. True or false Created by Mr. Lafferty Maths Dept.

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