1. Decimals
Math 6

2. Decimal Basics
Decimals

3. Decimal Basics Watch Brain Pop: Decimals
ations/decimals/

4. Decimal Basics How much of $1.00 does a Loonie represent?
1 whole of a dollar
1/1
1.00

5. One Whole

6. Decimal Basics
Whole Numbers on a Number Line

7. Decimal Basics How much of $1.00 does a dime represent?
1 tenth of a dollar
1/10
0.1

8. Decimal Basics
A whole separated into tenths

9. Decimal Basics

10. Decimal Basics

11. Decimal Basics
Comparison

12. Decimal Basics How much of $1.00 does a penny represent?
1 hundredth of a dollar
1/100
0.01

13. A whole separated into hundredths

14. Decimal Basics

15. Decimal Basics
Hundredths on a Number Line

16. Decimal Basics
Comparison of tenths and hundredths

17. Decimal Basics

18. Decimal Basics How much of $1.00 does a nickel represent?
5 hundredth of a dollar
5/100
0.05

19. Decimal Basics

20. Decimal Basics
Fifths on a Number Line

21. Decimal Basics How much of $1.00 does a quarter represent?
25 hundredth of a dollar
25/100
0.25

22. Decimal Basics

23. Decimal Basics
Twenty-fifths on a Number Line

24. Decimal Basics
A whole separated into thousandths

25. Decimal Basics

26. Decimal Basics

27. Decimal Basics

28. Decimal Basics

29. Decimal Basics

30. Decimal Basics
= three AND two hundred sixty-eight thousandths, five hundred seventy-nine millionths 3 . 2 6 8 5 7 9
ones
and
10ths
100ths
1000ths
10,000ths
100, 000ths
1000,000ths

31. Decimal Basics Key Points Represents less than one whole number
As we move right (on a PVC), each position is 10 times smaller
There is NO oneths spot (on a PVC)
Are “read” in the same way as whole numbers

32. Decimals and Fractions

33. Decimal & Fractions
BIG IDEA Decimals and Fractions are different ways of showing the same value

34. Decimal & Fractions A fraction is a part of a whole
We call the top number the Numerator, it is the number of parts you have
We call the bottom number the Denominator, it is the number of parts the whole is divided into

35. Decimal & Fractions Decimal Fraction 0.01 1/100 0.05 5/100 0.1 10/100
0.25
25/100
0.5
50/100
0.75
75/100
0.8
80/100
0.9
90/100
0.99
99/100

36. Decimal & Fractions Use your calculator
The easiest way to convert a fraction to a decimal is to divide the top number by the bottom number
divide the numerator by the denominator in mathematical language
63/100 = 0.63

37. Multiplying Decimals by Whole Numbers

38. Multiplying Decimals by Whole Numbers
What you know
When whole numbers are multiplied the product is always greater
Ex. 5 x 10 = 50

39. Multiplying Decimals by Whole Numbers
Do you see a pattern in the table?
x 1
 = 
0.2658
x 10
2.658
x 100
26.58
x 1,000
265.8
x 10,000
2,658.
x 100,000
26,580.
x 1,000,000
265,800.

40. Multiplying Decimals by Whole Numbers
In the Table the decimal is being multiplied by multiples of 10. (10, 100, 1000, 10,000)
Each time we multiply by a multiples of 10, the decimal point is moved one place to the right.
When decimals are multiplied by multiples of 10, the product is greater than the decimal being multiplied
Ex. 2.8 x 10 = 28

41. Multiplying Decimals by Whole Numbers
Rule:
For every 0 the decimal shifts one spot to the right

42. Multiplying Decimals by Whole Numbers
An electrician earns $18.75 per hour. If he worked 200 hours this month, then how much did he earn?

43. Multiplying Decimals by Whole Numbers
METHOD 1 – The decimal is greater than one
Step 1: Estimate
$ > 20.00
$20 x 200 = $4000
Your solution should be around $4000

44. Multiplying Decimals by Whole Numbers
METHOD 1 – The decimal is greater than one
Step 2: Multiply
Multiply the numbers as if they were whole numbers (remove the decimal)
1875 x 200 =

45. Multiplying Decimals by Whole Numbers
METHOD 1 – The decimal is greater than one
Step 3: Replace the decimal
Use the estimate ($4000)
replace the decimal to around decimal amount

46. Multiplying Decimals by Whole Numbers
The electrician earned $ for the month

47. Multiplying Decimals by Whole Numbers
TRY THESE – Use all 3 steps to solve
2 x 1.43
2 x 5.34
6 x 3.95

48. Multiplying Decimals by Whole Numbers
Stefan drinks a glass of pure orange juice each morning. The Orange Juice contains 0.054g of Vitamin C per glass.
How much Vitamin C does Stefan get from orange juice each week?

49. Multiplying Decimals by Whole Numbers
METHOD 2 – The decimal is less than one
Step 1: Remove the decimal (Jump Out)

50. Multiplying Decimals by Whole Numbers
METHOD 2 – The decimal is less than one
Step 2: Multiply
Multiply the numbers as if they were whole numbers
54 x 7 = 378

51. Multiplying Decimals by Whole Numbers
METHOD 2 – The decimal is less than one Step 3: Replace the decimal (Jump In)

52. Multiplying Decimals by Whole Numbers
Stefan receives 0.378gof Vitamin C from Orange juice each week.

53. Multiplying Decimals by Whole Numbers
TRY THESE – Use all 3 steps to solve
2 x 0.243
4 x 0.034
6 x

54. Multiplying Decimals by Whole Numbers

55. Multiplying Decimals by Whole Numbers
Project Preview: Determine the amount of each base ten block

56. 1.0

57. 0.1

58. Multiplying Decimals by Whole Numbers
Project Preview
0.01

59. Multiplying Decimals by Whole Numbers
Project Preview

60. Multiplying Decimals by Whole Numbers
Project Preview
Using the image as a guide, try to model the following decimal
2.23

61. Multiplying Decimals by Whole Numbers

62. Multiplying Decimals by Whole Numbers
Project Preview
Using the image as a guide, try to model the following decimal multiplication
1.35 x 4 = 5.4

63. Multiplying Decimals by Whole Numbers

64. Dividing Decimals by Whole Numbers
Decimals, Fractions, Percent

65. Dividing Decimals by Whole Numbers
What you know
When whole numbers are divided the quotient is always less
Ex. 50 ÷ 10 = 5

66. Dividing Decimals by Whole Numbers
Do you see a pattern in the table?
÷ 1
 = 
÷10
÷ 100
÷ 1,000
÷ 10,000
÷ 100,000
÷ 1,000,000

67. Dividing Decimals by Whole Numbers
In the Table the decimal is being divided by multiples of 10. (10, 100, 1000, 10,000)
Each time we divided by a multiple of 10, the decimal point is moved one place to the left.
When decimals are divided by multiples of 10, the quotient is less than the decimal being divided
Ex. 2.8 ÷ 10 = 0.28

68. Dividing Decimals by Whole Numbers
Rule:
For every 0 the decimal shifts one spot to the left

69. Dividing Decimals by Whole Numbers
There are three types of decimals:

70. Dividing Decimals by Whole Numbers
Terminating decimals stop at some point (aka rational)
0.125
3.75
2.125

71. Dividing Decimals by Whole Numbers
Repeating decimals repeat forever, but there is a pattern to their repetition
/ 5.3
/ 0.36
/ 1.834

72. Dividing Decimals by Whole Numbers
Non-recurring decimals are decimals that go on forever, but there is no pattern …

73. Dividing Decimals by Whole Numbers
There are NO remainders when dividing decimals

74. Dividing Decimals by Whole Numbers
Using LONG DIVISION to divide decimals 9.45 ÷ 4

75. Dividing Decimals by Whole Numbers
Using LONG DIVISION to divide decimals 10.4 ÷ 3

76. Dividing Decimals by Whole Numbers
Using LONG DIVISION to divide decimals 3.1 ÷ 7
7 3.1

77. Dividing Decimals by Whole Numbers
Often a decimal umber needs to be rounded. There are several factors to consider:
Money is ALWAYS rounded to the nearest 100th
Are there instructions? (Round to the nearest thousandth)
What are you measuring? (Kilometers, inches, Litres)
General rule is 2-3 decimal spots

78. Dividing Decimals by Whole Numbers
Rochelle entered 3 frogs into the Frog Olympics.
The total distance the frogs travelled was 4.92m.
About how far did each frog travel?

79. Dividing Decimals by Whole Numbers
METHOD 1 – The decimal is greater than one
Step 1: Estimate
Think… the number needs to be a multiple of 3
4.92 -> 6 (or 3)
6 ÷ 3 = 2
Your solution should be around 2

80. Dividing Decimals by Whole Numbers
METHOD 1 – The decimal is greater than one
Step 2: Divide
Divide the numbers as if they were whole numbers (remove the decimal)
492 ÷ 3 = 164

81. Dividing Decimals by Whole Numbers
METHOD 1 – The decimal is greater than one
Step 3: Replace the decimal
Use the estimate from step 1 (2)
replace the decimal
1.64

82. Dividing Decimals by Whole Numbers
Each frog traveled about 1.64m

83. Dividing Decimals by Whole Numbers
TRY THESE – Use all 3 steps to solve
16.64 ÷ 4
9.45 ÷ 5
62.8 ÷ 8

84. Dividing Decimals by Whole Numbers
Quincy has 0.926m of string. Suppose he cuts the string into 4 equal lengths. What is the length of each piece of string?

85. Dividing Decimals by Whole Numbers
METHOD 2 – The decimal is less than one Step 1: Remove the decimal (Jump Out)