1. 5th Grade Decimal Concepts
Mrs. Berish

2. Table of Contents Define and Review Vocabulary Identify Place Values
Click on a topic
to go to that section.
Identify Place Values
Read and Write Decimals
Compare and Order Decimals
Round Numbers to Designated Place Values

3. Define and Review Vocabulary
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Table of
Contents

4. What is a decimal number?
Click to find out!
A Decimal Number (based on the number 10) contains a Decimal Point.

7. are needed to fill the blue block? 10
Yellow Rod
How many yellow rods
are needed to fill the blue block? 10
click
What is the value of a yellow
rod? one-tenth (0.1)
click
Teacher Instructions: Use this page for students to gain an understanding of what tenths and hundredths look like.
Blue Block
Red Block
One Unit
(1)
How many red blocks are needed to fill the blue block? 100
(Hint: Fill a yellow rod with red blocks)
What is the value of a red block?
one-hundredth (0.01)
click
click

8. 3 yellow blocks = 0.3
three tenths
Blue = One Unit

9. twenty three hundredths
23 red blocks = 0.23
twenty three hundredths
Blue = One Unit

10. Interactive Number Grid - Use to Show Decimals
Click to Go to Interactive Site

11. 1
If the square equals one whole, what does the shaded area represent?

12. 2
If the square equals one whole, what does the shaded area represent?

13. 3
If the square equals one whole, what does the shaded area represent?

14. 4
If the square equals one whole, what does the shaded area represent?

15. 5
If the square equals one whole, what does the shaded area represent?

16. Identify Place Values
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Table of
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17. Place Value
As you look at the place value chart, how many times does the value of the number increase as you go to the left?
click for answer
Each place has a value that is 10 times the value of its place to the right.

18. Place Value
As you look at the place value chart, how many times does the value of the number increase as you go to the right?
click for answer
Each place has a value that is ten times smaller than the value of its place to its left.

19. Place
Value
Chart
Teacher Instructions: NOTE: CAN BE PRINTED FOR STUDENT USE

20. What digit is in the hundreds place? 987,654.0123B 2 C 1 D 7

21. What digit is in the thousandths place? 987,654.0123B 2 C 3 D 8

22. What digit is in the tenths place? 987,654.0123B 4 C D 5

23. What digit is in the ten thousands place? 987,654.0123B 7 C 4 D 8

24. What digit is in the hundredths place? 987,654.012310
What digit is in the hundredths place?
987, A 5 B C 1 D 2

25. Decimals on the number line3 2
What does each line represent on this number line between the whole numbers of 2 and 3?
Label the number line.

26. Decimals on the number line32 33
What does each line represent on this number line between the whole numbers of 32 and 33?
Label the number line.

27. Decimals on the number line
4.3
4.4
What does each line represent on this number line between the decimal numbers of 4.3 and 4.4?
Label the number line.

28. Decimals on the number line
0.63
0.64
What does each line represent on this number line between the decimal numbers of 0.63 and 0.64?
Label the number line.

29. Decimal Number Lines Tool Click for instructions
and to use the tool.

30. National Library of Virtual Manipulatives Click to go to web site.
Change Places to
"Decimals"
at the bottom left.
Zoom in to drag the dot more precisely.

31. Where would the number 4.4 go on this number line?11
Where would the number 4.4 go on this number line? A B C D 10

32. Where would the number 6.8 go on this number line?12
Where would the number 6.8 go on this number line? A B C D 10

33. Where would the number 0.8 go on this number line?13
Where would the number 0.8 go on this number line? A B C D 1

34. Where would the number 7.2 go on this number line?14
Where would the number 7.2 go on this number line? 7 A B C D 8

35. Where would the number 19.3 go on this number line?15
Where would the number 19.3 go on this number line? 19 A B C D 20

36. Where would the number 324.5 go on this number line?16
Where would the number go on this number line?
324 A B C D
325

37. Where would the number 5.35 go on this number line?17
Where would the number 5.35 go on this number line? A B C D
5.4
5.3

38. Where would the number 1.08 go on this number line?18
Where would the number 1.08 go on this number line? 1 A B C
1.1 D
Not on this number line

39. Where would the number 6.23 go on this number line?19
Where would the number 6.23 go on this number line?
6.2 A B C
6.3 D
Not on this number line

40. Where would the number 17.04 go on this number line?20
Where would the number go on this number line?
17.1 A B C
17.2 D
Not on this number line

41. Read and Write Decimals
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Table of
Contents

42. 9, 8 7 5, 6 1 . 4 9 hundred thousand ten thousandth ten thousand
million
hundred thousand
ten thousand
thousand
hundred
ten
one
and
tenth
hundredth
thousandth
ten thousandth 9, 8 7 5, 6 1 . 4 9
This number is read:
Nine million, eight hundred seventy-five thousand, six hundred ten AND four hundred seventy-nine thousandths
Remember the place values after the decimal point start with tenths

43. × Can you read the number? hundredths thousandths thousands hundreds
tenths
tens
ones
and × . 7 5 4 6 2 9 8 3 1

44. Read the following numbers.
6.16
0.052 2,
6.371
0.03
645.16
2,104.03
0.004
403.5
83,

45. How do you write a decimal in words?
1. Look to see if there is a number to the left of the decimal; if so write it out. If there is no number to the left of the decimal, skip to step 3.
2. Write an and for the decimal point.
3. Write the number in the decimal part.
4. Write the word for the place value of the rightmost digit.
Write in words
click
Thirteen and twenty-four hundredths

46. × How does a comma help when writing a decimal number?
The place value before the comma is always stated.
For example:
1,547 is written
One THOUSAND, five hundred forty-seven
6,547,100 is written
6 MILLION, five hundred forty-seven THOUSAND, 
one hundred ×

47. Write the decimal in words×
1) Five and four hundredths
2) One hundred forty-six and four hundred fifty-seven thousandths
3) Nine ten-thousandths
4) 6, Six thousand, three hundred forty-five
and one hundred forty-nine thousandths

48. Match each number and written form.
four thousand and fifty three
405.3
forty and fifty three hundredths
4.53
four thousand fifty three
40.53
four hundred five and three tenths
none
four and fifty three thousandths
4.053
forty and fifty three hundredths
4,053

49. 21 What is 4.36 in written form? A four and thirty six B
four and thirty six tenths C
four, thirty six D
four and thirty six hundreths

50. 22 What is 63.067 in written form? A
sixty three and sixty seven hundredths B
sixty three and sixty seven thousandths C
sixty three and sixty seven D
sixty three, sixty seven thousandths

51. 23 What is 0.419 in written form? A zero and four hundred nineteen B
four hundred nineteen hundredths C
four hundred nineteen thousandts D
four one nine

52. 24 What is 0.09 in written form? A nine and nine B nine hundredths C
nine and nine hundredths D
nine and zero nine tenths

53. 25 What is 407.021 in written form? A four zero seven zero two one B
nine and nine tenths C
four hundred seven and twenty one thousandths D
four hundred seven and twenty one hundredths

54. Writing a decimal numerically×
1. If there is a ths, there will be a decimal
2. If there is an and, there will be a whole number to the left of the decimal
3. Note the ending - this is the place where the decimal number will end
4. Use the decimal chart to help you!

55. Use the chart as a guide to write the decimal numbers
hundredths
thousandths
thousands
hundreds
tenths
tens
ones
and
1. two hundred sixteen and 2 tenths
2. thirty two and nine thousandths
3. four thousand, five hundred six and twenty four hundredths
4. nine hundred and eight hundredths

56. What is fifty two and eighteen hundredths?26
What is fifty two and eighteen hundredths? A
52,18 B
52.018 C
52.18 D

57. What is five thousand fifty and five hundredths?27
What is five thousand fifty and five hundredths? A
550.5 B
5,050.5 C
5,050.05 D
5,500.05

58. What is six hundred three and four thousandths?28
What is six hundred three and four thousandths? A
603.4 B C
603.04 D

59. What is thirty four hundredths?29
What is thirty four hundredths? A
340 B 34 C
0.34 D
0.034

60. What is four hundred ninety five thousandths?30
What is four hundred ninety five thousandths? A
495 B C
0.0495 D
0.495

61. Compare and Order Decimals
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Table of
Contents

62. There are two symbols we use to compare numbers.
> (greater than)
< (less than)
One number goes on the left of the symbol and another number goes on the right of the symbol.
The number on the left of the ">" shows the larger number.
For example: 2 > 1
The number on the left of the "<" shows the smaller number.
For example: 1 < 2

63. Symbols and Words to remember when comparing numbers
greater than/largest
>
<
less than/ smallest =
equal

64. Comparing Decimals Line up the decimal points
Put zeros in wherever digits are missing
Compare the digits, from left to right
The largest digit, having the same place value, names the largest number

65. Compare left to right. 2 is greater than 0, so 0.21 is greatest.
Compare and 0.21
Line up the decimal points
Put zeros in wherever digits are missing
Compare the digits, from left to right
The largest digit, having the same place value, names the largest number
0.045
0.210
put zero
on the
end
Compare left to right. 2 is greater than 0, so 0.21 is greatest.
Click
0.045 < 0.21

66. 0.36 > 0.312 Compare 0.36 and 0.312 Line up the decimal points
Put zeros in wherever digits are missing
Compare the digits, from left to right
The largest digit, having the same place value, names the largest number
put zero
on the
end
0.360
0.312
Compare left to right.
6 is greater than 1,
so 0.36 is greatest.
Click
0.36 > 0.312

67. 0.009 < 0.02 Compare 0.009 and 0.02 Line up the decimal points
Put zeros in wherever digits are missing
Compare the digits, from left to right
The largest digit, having the same place value, names the largest number
0.009
0.020
put zero
on the
end
Compare left to right.
2 is greater than 0,
so 0.02 is greatest.
Click
0.009 < 0.02

68. Decimal Squares Interactive Games Click for link.
Game could also be played with two students having a spinner and writing down their decimal number.
In this game the robot won because is greater than

69. 31
Choose the correct symbol. A
> B
< C =

70. 32
Choose the correct symbol. A
> B
< C =

71. 33
Choose the correct symbol. A
> B
< C =

72. 34
Choose the correct symbol. A
> B
< C =

73. 35
Choose the correct symbol. A
> B
< C =

74. × Ordering Decimals Line up all of the decimal points
Put zeros in wherever digits are missing
Compare the digits, from left to right
The largest digit, having the same place value, names the largest number
Example: ×
Why is
this the
smallest number?
What digit tells us this is the largest number?
Click 1
Compare the digits

75. The number with the least value is:36
The number with the least value is: A
61.005 B
61.3 C
61.05 D
61.04

76. The number with the least value is:37
The number with the least value is: A
0.005 B
0.5 C
0.05 D
0.0005

77. The number with the greatest value is:38
The number with the greatest value is: A
9.888 B
9.8 C
9.008 D
9.088

78. The number with the greatest value is:39
The number with the greatest value is: A
0.67 B
0.067 C
0.0067 D

79. How much money would you like to win?40
How much money would you like to win? A
$150.59 B
$140.99 C
$150.82 D
$140.50

80. Rewrite the numbers to order them from least to greatest.
15, 0, 1.5, 0.015, 0.15

81. Rewrite the numbers to order them from least to greatest.
0.709, 0.009, 0.68, 0.08, 0.07

82. Which of the following is ordered least to greatest?41
Which of the following is ordered least to greatest? A
0.3, 0.03, 0.33, 3.3 B
0.03, 0.3, 0.33, 3.3 C
3.3, 0.33, 0.3, 0.03

83. Which of the following is ordered least to greatest?42
Which of the following is ordered least to greatest? A
0.008, 0.06, 0.5 B
0.5, 0.06, 0.008 C
0.06, 0.5, 0.008

84. Which of the following is ordered greatest to least?43
Which of the following is ordered greatest to least? A
8.07, 0.008, 0.087, 0.87 B
0.008, 0.087, 0.87, 8.07 C
8.07, 0.87, 0.087, 0.008

85. Which of the following is ordered greatest to least?44
Which of the following is ordered greatest to least? A
0.23, 0.08, 0.009 B
0.23, 0.009, 0.08 C
0.009, 0.08, 0.23

86. Which of the following is ordered least to greatest?45
Which of the following is ordered least to greatest? A
0.8, 0.32, 0.41, 0.701 B
0.8, 0.701, 0.41, 0.32 C
0.32, 0.41, 0.701, 0.8

87. Round Numbers to Designated Place Values
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Table of
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88. Rounding makes numbers that are easier to work with in your head.
Rounded numbers are only approximate.
An exact answer generally can not be obtained using rounded numbers.
Use rounding to get an answer that is close but that does not have to be exact.

89. Round 8,749 to the nearest ten.
Review
Round 8,749 to the nearest ten.
1. Put your pencil point under the digit in the tens place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the tens place?
Those digits always remain the same.
5. What happens to everything to the right of the tens place?
Those digits become zero.
Teacher Instructions: Move pencil under the digit that is being rounded to rounding

90. Round 8,749 to the nearest hundred.
Review
Round 8,749 to the nearest hundred.
1. Put your pencil point under the digit in the hundreds place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the hundreds place?
Those digits always remain the same.
5. What happens to everything to the right of the hundreds place?
Those digits become zero.
Teacher Instructions: Move pencil under the digit that is being rounded to rounding

91. 46
Round 143 to the nearest ten

92. 47
Round 4,561 to the nearest hundred.

93. Round 564,012 to the nearest hundred thousand.48

94. Round 7,399 to the nearest thousand.49

95. Round 63,752 to the nearest hundred.50

96. What happens in this case?
Round 697 to the nearest ten.
The 7 to the right of the 9 tells us to increase the 9 by 1.
What happens?
Answer ____________

97. Round 3,972 to the nearest hundred.51

98. Round 98 to the nearest ten.52

99. Round 399,238 to the nearest ten thousand.53

100. Round 9,521 to the nearest thousand.54

101. Round 9,983 to the nearest hundred.55

102. Rounding Decimals
Let's learn how to round decimals using the following examples:
Round to the nearest tenths place.
When rounding decimals, put your pencil point under the place value that you are rounding to
DO NOT MOVE IT

103. 687.268 1. Put your pencil point under the digit in the tenths place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the tenths place?
Those digits always remain the same.

104. 5. What happened to the digits to the right of the tenths place?
Remember, we are rounding.
The place values to the right of the tenths place have zero value, so now the digits 6 and 8 become zeroes.
= 687.3
However we leave the zeros off when they are to the right of the decimal point.

105. Round 8.73258 to the hundredths place.
1. Put your pencil point under the digit in the hundredths place.
Look to the right.
2. Is the digit 5 or more?
Yes OR No
3. What happens to the digit?
Increases by 1 OR remains the same
4. What happens to everything to the left of the hundredths place?
Those digits always remain the same.
5. What happens to everything to the right of the hundredths place?
Those digits become zero (and we leave them off since they are to the right of the decimal).

106. Round 687.4953 to the nearest hundredths place Answer: 687.50
Try this:
Round to the nearest hundredths place
Answer:
click

107. 56
Round
to the nearest hundredth.

108. 57
Round
to the nearest ten.

109. 58
Round
to the nearest hundred.

110. 59
Round
to the nearest tenth.

111. 60
Round
to the nearest thousand.

112. 61
Round
to the nearest thousandth.

113. Caution!
When rounding to a specific place, your answer MUST have a digit in that place.
Example:
Round to the nearest tenth
Answer: 24.0
There must be a digit in the tenths place, since we were to round to the tenths place.

114. 62
Round
678.97
to the nearest tenth.

115. 63
Round
6.304
to the nearest hundredth.

116. 64
Round
5.03
to the nearest tenth.

117. 65
Round
0.3497
to the nearest thousandth.

118. 66
Round
84.951
to the nearest tenth.

119. Use rounding to estimate answers to problems.
At a restaurant, a burger is $5.99, fries are $3.85 and a small drink is $1.29. Round to the nearest dollar to estimate the cost to purchase all three items.
Cost Estimate
$5.99 $6
$3.85 $4
$1.29 $1
It would cost about $11 to purchase all three items.

120. 67
Round the following items to the nearest dollar to figure out the approximate cost if all the items were bought.
pens $2.99
pencils $2.20
book bag $15.75

121. 68
Round the following items to the nearest dollar to figure out the approximate cost if all the items were bought.
jeans $24.99
t-shirt $6.79
hat $12.31

122. 69
Round the following items to the nearest dollar to figure out the approximate cost if all the items were bought.
milk $3.79
bread $2.15
juice $2.40

123. 70
Round the following items to the nearest half dollar to figure out the approximate cost if all the items were bought.
chicken $8.60
potatoes $2.45
peas $0.99

124. 71
Round the following items to the nearest half dollar to figure out the cost if all the items were bought.
apples $4.60
bananas $1.90
oranges $3.10

125. 72
Round the following items to the nearest ten dollars to figure out the approximate cost if all the items were bought.
sneakers $36.21
sweatshirt $13.99
socks $6.00

126. 73
Round the following items to the nearest hundred dollars to figure out the approximate cost if all the items were bought.
computer $688.23
printer $213.50
desk $175.89