1. Decimals

2. 1. Demonstrate skills in using place value and mental math. 2
1. Demonstrate skills in using place value and mental math Perform calculations involving addition and subtraction of decimals Perform calculations involving multiplication with decimals Perform calculations involving division with decimals Perform calculations involving comparison, ordering, and estimation with decimals

3. Place Value

5. Write the name of the decimal place indicated: 725

6. Answer: ones (also called the units digit)

7. Write the name of the decimal place indicated: 11,717,555

8. Answer: ten thousands

9. Write the name of the decimal place indicated: 9,053,496

10. Answer: hundreds

11. Write the name of the decimal place indicated: 105,016

12. Answer: thousands

13. Write the name of the decimal place indicated: 43,105

14. Answer: tens

15. Write the name of the decimal place indicated: 8.68354

16. Answer: ten-thousandths

17. Write the name of the decimal place indicated: 9.6456

18. Answer: thousandths

19. Write the name of the decimal place indicated: 1.87605

20. Answer: hundredths

21. Write the name of the decimal place indicated: 7.111

22. Answer: tenths

23. Write the name of the decimal place indicated: 32.658297

24. Answer: hundred-thousandths

25. Write the name of the decimal place indicated: 639,606,650

26. Answer: hundred millions

27. Round to the place indicated: 9,885,659,260 billions

28. Answer: 10,000,000,000

29. Round to the place indicated: 2,628,259 thousands

30. Answer: 2,628,000

31. Round to the place indicated: 1.7354948 hundred-thousandths

32. Answer:

33. Round to the place indicated: 6.3761 tenths

34. Answer: 6.4

35. Adding and Subtracting Decimals

36. Rules for Addition Line up your decimal points.
Add 0s after the decimal point so that all of the numbers have the same number of places after the decimal.
Add as you would with whole numbers.
Just move the decimal point down into your answer.

37. Rules for Addition - Example
Line up your decimal points
_______________________________
Add 0s after the decimal point so that all of the numbers have the same number of places after the decimal
______________________________

38. Rules for Addition - Example
Add as you would with whole numbers.
______________________________
Move the decimal point down into your answer.

39. Rules for Subtraction Line up your decimal points.
Add 0s after the decimal point so that all of the numbers have the same number of places after the decimal.
Subtract as you would with whole numbers.
Just move the decimal point down into your answer.

40. Rules for Subtraction - Example
Line up your decimal points.
_____________________________________
Add 0s after the decimal point so that all of the numbers have the same number of places after the decimal.
____________________________________

41. Rules for Subtraction - Example
Subtract as you would with whole numbers.
______________________________________
Keep the decimal point in your answer in the same spot as in you problem.

42. Evaluate the following expression: 13.7 + 3.2

43. Answer:

44. Evaluate the following expression: 3.305 + 1.7

45. Answer:

46. Evaluate the following expression: 9.8 − 7.1

47. Answer: 2.7

48. Evaluate the following expression: 15.5 − 15.5

49. Answer: 0

50. Evaluate the following expression: 5.4 + (−9.7)

51. Answer: −4.3

52. Evaluate the following expression: 10.8 + (−4.73)

53. Answer:

54. Evaluate the following expression: (−0.5) + 0.3

55. Answer: −0.2

56. Evaluate the following expression: (−4.79) + (−0.4)

57. Answer: −5.19

58. Evaluate the following expression: (−10.9) + 6.1

59. Answer: −4.8

60. Evaluate the following expression: 2.2 − 7.3

61. Answer: −5.1

62. Evaluate the following expression: (−8.1) − (−8.9)

63. Answer: 0.8

64. Evaluate the following expression: (−3.9) − 8.9

65. Answer: −12.8

66. Evaluate the following expression: (−18.278) − (−6.8)

67. Answer: −11.478

68. Evaluate the following expression: 1.81 − 17.17

69. Answer: −15.36

70. Evaluate the following expression: 8.7 + 3.8 + 12.3

71. Answer:

72. Evaluate the following expression: (−13.6) + 12 − (−15.5)

73. Answer:

74. Evaluate the following expression: 3.4 − 5 − 10.4

75. Answer: −12

76. Evaluate the following expression: (−5.6) − (−12.6) + (−6.6)

77. Answer: 0.4

78. Multiplying Decimals

79. Rules for Multiplication
Line up your numbers with the last digits under each other.
Multiply as you would with whole numbers.
Add the decimal places in each of the numbers being multiplied.
Move the decimal point to the left the TOTAL number of places in the numbers being multiplied.

80. Rules for Multiplication - Example
Line up your numbers with the last digits under each other. x
_____________________________________

81. Rules for Multiplication - Example
Multiply as you would with whole numbers.
1 2.3 x
_____________________________________
1 2 3
______________________________________

82. Rules for Multiplication - Example
Add the decimal places in each of the numbers being multiplied.
decimal place
x decimal places
_____________________________________ _________________________________________________
1 2 3
NEEDS
______________________________________
decimal places

83. Rules for Multiplication - Example
Move the decimal point to the left the TOTAL number of places in the numbers being multiplied.
decimal place
x decimal places
_____________________________________ _________________________________________________
1 2 3
NEEDS
______________________________________
decimal places

84. Rules for Multiplication - Example
BIG HINT:
Check your answer using just whole numbers to make sure your answer is reasonable and the decimal point is in the correct place.
12 x 6 = 72 so is reasonable
Would be reasonable?
Would be reasonable?
Would 7,515.3 be reasonable?

85. Evaluate the following expression: 0.2 ∙ (-1.6)

86. Answer:

87. Evaluate the following expression: -1.5 ∙ (-7.1)

88. Answer:

89. Evaluate the following expression: -4.6 ∙ (-7.2)

90. Answer:

91. Evaluate the following expression: −5.5 ∙ −4.87

92. Answer:

93. Evaluate the following expression: −5.928 ∙ −11.6

94. Answer:

95. Evaluate the following expression: −7.5 ∙ 9 ∙ −8.3

96. Answer:

97. Evaluate the following expression: 8.1 ∙ 8.6 ∙ −5.2

98. Answer: −

99. Dividing Decimals

100. Rules for Division
Move the decimal point in the divisor (the number outside the box) to the right to make it a whole number.
Move the decimal point in the dividend (the number inside the box) to the right the same number of places.
Divide as you would with whole numbers.
Move the decimal point into the quotient (your answer) directly above the decimal point you moved in the dividend.

101. Rules for Division – Example
Move the decimal point in the divisor (the number outside the box) to the right to make it a whole number.
Move the decimal point one point to the right
Becomes

102. Rules for Division – Example
Divide as you would with whole numbers
3 6
Ignore the decimal point for now!
- 4 8
9 6
Move the decimal point into the quotient (your answer) directly above the decimal point you moved in the dividend.
3.6

103. Division – Another Example
What happens to the dividend when there are no more numbers to move the decimal place to?
Example 1: ÷ 1.6 OR
Since there is one decimal place in the divisor, we need to move the decimal point in the dividend and the divisor to the right one.
How can we do this?
Remember we can add 0s after the decimal point without changing the value of the number.

104. Division – Another Example
Now we can solve as usual.
becomes
Which equals 5
0 .

105. Division – Another Example
7.15 ÷ or
Move the decimal places one place to the right.
.2 2
6 5 0

106. Rules for Division - Example
BIG HINT:
Check your answer using just whole numbers to make sure your answer is reasonable and the decimal point is in the correct place.
5 / 1 = 5 or
6 / 2 = 3 (if you round to a whole number)
so 3.6 is reasonable
Would .36 be reasonable?
Would 36 be reasonable?

107. Evaluate the following expression: 0.3 ÷ 0.1

108. Answer: 3

109. Evaluate the following expression: -0.3 ÷ 0.01

110. Answer: - 30

111. Evaluate the following expression: -0.25 ÷ (-0.75)

112. Answer: ___ 0.33

113. Evaluate the following expression: 0.23 ÷ (-0.02)

114. Answer: