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5th Grade
Decimal Concepts
2012-09-04
www.njctl.org
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Use Slide Show View to Administer Assessment Items
To administer the numbered assessment items in this presentation, use
the Slide Show view. (See Slide 11 for an example.)
Table of Contents
Define and Review Vocabulary
Identify Place Values
Read and Write Decimals
Compare and Order Decimals
Round Numbers to Designated Place Values
Click on a topic
to go to that section.
Define and Review Vocabulary
Return to
Table of
Contents
What is a decimal number?
Click to find out!
A Decimal Number (based on the number 10)
contains a Decimal Point.
Yellow Rod
How many yellow rods
click
are needed to fill the blue block? 10
What is the value of a yellow
click
rod? one-tenth
(0.1)
Blue Block
One Unit
(1)
Red Block
How many red blocks are needed to fill
the blue block? Click
100
(Hint: Fill a yellow rod with red blocks)
What is the value of a red block?
one-hundredth
(0.01)
click
3 yellow blocks = 0.3
three tenths
Blue = One Unit
23 red blocks = 0.23
twenty three hundredths
Blue = One Unit
Interactive Number Grid - Use to Show Decimals
Click to Go to Interactive Site
1
If the square equals one whole, what does the
shaded area represent?
2
If the square equals one whole, what does the
shaded area represent?
3
If the square equals one whole, what does the
shaded area represent?
4
If the square equals one whole, what does the
shaded area represent?
5
If the square equals one whole, what does the
shaded area represent?
Identify Place Values
Return to
Table of
Contents
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?
Each place has a value that is 10 times the value of its place to the
right.
click for answer
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?
Each place has a value that is ten times smaller than the value of its
place to its left.
click for answer
Place
Value
Chart
6
What digit is in the hundreds place?
987,654.0123
A
6
B
C
2
1
D
7
7
What digit is in the thousandths place?
987,654.0123
A
7
B
C
2
3
D
8
8
What digit is in the tenths place?
987,654.0123
A
1
B
C
4
0
D
5
9
What digit is in the ten thousands place?
987,654.0123
A
3
B
C
7
4
D
8
10
What digit is in the hundredths place?
987,654.0123
A
5
B
C
0
1
D
2
Decimals on the number line
2
3
What does each line represent on this number line between the whole
numbers of 2 and 3?
Label the number line.
Decimals on the number line
32
33
What does each line represent on this number line between the whole
numbers of 32 and 33?
Label the number line.
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.
Decimals on the number line
What does each line represent on this number line between the
decimal numbers of 0.63 and 0.64?
Label the number line.
Decimal Number Lines Tool
Click for instructions
and to use the tool.
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.
11
Where would the number 4.4 go on this number
line?
0
A B C D
10
12
Where would the number 6.8 go on this number
line?
0
A B C
D
10
13
Where would the number 0.8 go on this number line?
0
A
B
C
D
1
14
Where would the number 7.2 go on this number
line?
7A
B
C
D
8
15
Where would the number 19.3 go on this
number line?
19 A
B
C
D
20
16
Where would the number 324.5 go on this number
line?
A
B C
D
17
Where would the number 5.35 go on this number line?
5.3
A
B
C
D
5.4
18
Where would the number 1.08 go on this number
line?
B
1 A
D
Not on this number line
C
1.1
19
Where would the number 6.23 go on this
number line?
6.2
A
D
B
C
Not on this number line
6.3
20
Where would the number 17.04 go on this number
line?
17.1
A
B
D
C
Not on this number line
17.2
Read and Write Decimals
Return to
Table of
Contents
9,
8 7
5,
6 1 0
.
4
7
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
Can you read the number?
5
2
3
4
5
0
.
0
7
6
.
2
5
8
.
3
0
.
8
9
0
.
0
1
4
.
6
9
.
7
×
9
1
Read the following numbers.
6.16
645.16
0.052
2,104.03
2,104.371
0.004
6.371
403.5
0.03
83,042.004
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 13.24 in words
click
Thirteen
and twenty-four hundredths
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
×
Write the decimal in words
1) 5.04
Five and four hundredths
2)
One hundred forty-six and four hundred fifty-seven
thousandths
146.457
3) .0009
Nine ten-thousandths
4) 6,345.149
Six thousand, three hundred forty-five
and one hundred forty-nine thousandths
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
21
What is 4.36 in written form?
A
four and thirty six
B
C
four and thirty six tenths
four, thirty six
D
four and thirty six hundreths
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
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
24
What is 0.09 in written form?
A
nine and nine
B
C
nine and nine tenths
nine and nine hundredths
D
nine and zero nine tenths
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
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!
×
Use the chart as a guide to write the decimal numbers
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
26
What is fifty two and eighteen hundredths?
A
52,18
B
C
52.018
52.18
D
52.0018
27
What is five thousand fifty and five hundredths?
A
550.5
B
5,050.5
C
5,050.05
D
5,500.05
28
What is six hundred three and four thousandths?
A
603.4
B
C
603.004
603.04
D
603.0004
29
What is thirty four hundredths?
A
340
B
C
34
0.34
D
0.034
30
What is four hundred ninety five thousandths?
A
495
B
C
495.000
0.0495
D
0.495
Compare and Order Decimals
Return to
Table of
Contents
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
Symbols and Words to remember
when comparing numbers
SYMBOL
WORDS
>
greater than/largest
<
less than/ smallest
=
equal
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
Compare 0.045 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 < 0.21
Click
0.045
0.210
put zero
on the
end
Compare left to right. 2 is
greater than 0, so 0.21 is
greatest.
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
0.36 > 0.312
Click
0.360
0.312
put zero
on the
end
Compare left to right.
6 is greater than 1,
so 0.36 is greatest.
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 < 0.02
Click
0.009
0.020
put zero
on the
end
Compare left to right.
2 is greater than 0,
so 0.02 is greatest.
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 0.7950 is greater than
0.5021
31
Choose the correct symbol.
A
>
B
<
C
=
0.41
0.049
32
Choose the correct symbol.
A
>
B
<
C
=
0.301
0.311
33
Choose the correct symbol.
A
>
B
<
C
=
0.007
0.05
34
Choose the correct symbol.
A
>
B
<
C
=
0.179
0.24
35
Choose the correct symbol.
A
>
B
<
C
=
0.46
0.6
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:
910.800
085.007
910.801
911.900
085.070
What digit tells us this is the
largest number?
Compare the digits
1
Click
×
Why is
this the
smallest
number?
36
The number with the least value is:
A
61.005
B
61.3
C
61.05
D
61.04
37
The number with the least value is:
A
0.005
B
0.5
C
0.05
0.0005
D
38
The number with the greatest value is:
A
9.888
B
9.8
C
9.008
D
9.088
39
The number with the greatest value is:
A
0.67
B
0.067
0.0067
0.00067
C
D
40
How much money would you like to win?
A
$150.59
B
$140.99
C
$150.82
D
$140.50
Rewrite the numbers to order them from least to greatest.
15, 0, 1.5, 0.015, 0.15
Rewrite the numbers to order them from least to greatest.
0.709, 0.009, 0.68, 0.08, 0.07
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
3.3, 0.33, 0.3, 0.03
C
42
Which of the following is ordered least to
greatest?
A
0.008, 0.06, 0.5
B
0.5, 0.06, 0.008
0.06, 0.5, 0.008
C
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
8.07, 0.87, 0.087, 0.008
C
44
Which of the following is ordered greatest to least?
A
0.23, 0.08, 0.009
B
0.23, 0.009, 0.08
0.009, 0.08, 0.23
C
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
0.32, 0.41, 0.701, 0.8
C
Round Numbers to
Designated Place Values
Return to
Table of
Contents
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.
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.
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.
46
Round 143 to the nearest ten
47
Round 4,561 to the nearest hundred.
48
Round 564,012 to the nearest hundred thousand.
49
Round 7,399 to the nearest thousand.
50
Round 63,752 to the nearest hundred.
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 ____________
51
Round 3,972 to the nearest hundred.
52
Round 98 to the nearest ten.
53
Round 399,238 to the nearest ten thousand.
54
Round 9,521 to the nearest thousand.
55
Round 9,983 to the nearest hundred.
Rounding Decimals
Let's learn how to round decimals using the following examples:
Round 687.268 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
687.268
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.
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.
687.300 = 687.3
However we leave the zeros off when they are to the right of the
decimal point.
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).
Try this:
Round 687.4953 to the nearest hundredths place
Answer: 687.50
click
56
Round
6874.6479
to the nearest hundredth.
57
Round
6874.6479
to the nearest ten.
58
Round
6874.6479
to the nearest hundred.
59
Round
6874.6479
to the nearest tenth.
60
Round
6874.6479
to the nearest thousand.
61
Round
6874.6479
to the nearest thousandth.
Caution!
When rounding to a specific place, your answer MUST have a digit in
that place.
Example:
Round 23.97 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.
62
Round
678.97
to the nearest tenth.
63
Round
6.304
to the nearest hundredth.
64
Round
5.03
to the nearest tenth.
65
Round
0.3497
to the nearest thousandth.
66
Round
84.951
to the nearest tenth.
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
$5.99
$3.85
$1.29
Estimate
$6
$4
$1
It would cost about $11 to purchase all three items.
67
Round the following items to the nearest dollar to
figure out the approximate cost if all the items were
bought.
pens
pencils
book bag
$2.99
$2.20
$15.75
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
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
70
Round the following items to the nearest half dollar
to figure out the approximate cost if all the items
were bought.
chicken
potatoes
peas
$8.60
$2.45
$0.99
71
Round the following items to the nearest half dollar to
figure out the cost if all the items were bought.
apples
bananas
oranges
$4.60
$1.90
$3.10
72
Round the following items to the nearest ten dollars
to figure out the approximate cost if all the items
were bought.
sneakers
sweatshirt
socks
$36.21
$13.99
$6.00
73
Round the following items to the nearest hundred
dollars to figure out the approximate cost if all the
items were bought.
computer
printer
desk
$688.23
$213.50
$175.89
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