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Define and Review Vocabulary
Identify Place Values
Read and Write Decimals
Compare and Order Decimals
Round Numbers to Designated Place Values
Table of Contents
Click on a topicto go to that section.
Define and Review Vocabulary
Return to Table of Contents
A Decimal Number (based on the number 10) contains a Decimal Point.
Click to find out!
What is a decimal number?
Blue BlockRed Block
How many yellow rods are needed to fill the blue block? 10
Yellow Rod
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)
One Unit (1)
click
What is the value of a yellow rod? one-tenth (0.1)click
click
click
Blue = One Unit
3 yellow blocks = 0.3three tenths
23 red blocks = 0.23twenty three hundredths
Blue = One Unit
Interactive Number Grid - Use to Show DecimalsClick 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
6
2
1
A
B
C
D 7
7
7
2
3
A
B
C
D 8
What digit is in the thousandths place? 987,654.0123
8 What digit is in the tenths place?
987,654.0123
1
4
0
A
B
C
D 5
9 What digit is in the ten thousands place?
987,654.0123
3
7
4
A
B
C
D 8
10 What digit is in the hundredths place?
987,654.0123
5
0
1
A
B
C
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
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.
Decimal Number Lines Tool
Click for instructions and to use the tool.
National Library of Virtual ManipulativesClick 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?
A B C D0 10
12 Where would the number 6.8 go on this number line?
A B C D0 10
13 Where would the number 0.8 go on this number line?
A B C D0 1
14 Where would the number 7.2 go on this number line?
A B C D7 8
15 Where would the number 19.3 go on this number line?
A B C D19 20
16 Where would the number 324.5 go on this number line?
A B C D
324
325
17 Where would the number 5.35 go on this number line?
A B C D5.3 5.4
18 Where would the number 1.08 go on this number line?
A B C
D Not on this number line
1 1.1
19 Where would the number 6.23 go on this number line?
A B C6.2 6.3
D Not on this number line
20 Where would the number 17.04 go on this number line?
A B C17.1 17.2
D Not on this number line
Read and Write Decimals
Return to Table of Contents
Remember the place values after the decimal point start with tenths
mill
ion
hu
nd
red
th
ou
san
dte
n t
ho
usa
nd
tho
usa
nd
hu
nd
red
ten
on
e
and
ten
th
hu
nd
red
thth
ou
san
dth
ten
th
ou
san
dth
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
0 . 0 7
5 4 6 . 2 5 9
8 . 3
0 . 8 9
0 . 0 1 1
2 3 5 4 . 6
9 . 7
Can you read the number?th
ou
san
ds
hu
nd
red
s
ten
s
on
es
and
ten
ths
hu
nd
red
ths
tho
usa
nd
ths
×
6.16
0.052
2,104.371
6.371
0.03
645.16
2,104.03
0.004
403.5
83,042.004
Read the following numbers.
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.
How do you write a decimal in words?
Write 13.24 in words
Thirteen and twenty-four hundredthsclick
How does a comma help when writing a decimal number?
The place value before the comma is always stated.
For example:
1,547 is writtenOne THOUSAND, five hundred forty-seven
6,547,100 is written6 MILLION, five hundred forty-seven THOUSAND, one hundred
×
Write the decimal in words
1) 5.04 Five and four hundredths
2) 146.457 One hundred forty-six and four hundred fifty-seven thousandths
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 fifty three
four hundred five and three tenths
forty and fifty three hundredths
four thousand and fifty three
four and fifty three thousandths
forty and fifty three hundredths
405.3
4.53
40.53
none
4.053
4,053
21 What is 4.36 in written form?
four and thirty six
four and thirty six tenths
four, thirty six
A
B
C
D four and thirty six hundreths
22 What is 63.067 in written form?
sixty three and sixty seven hundredths
sixty three and sixty seven thousandths
sixty three and sixty seven
A
B
C
D sixty three, sixty seven thousandths
23 What is 0.419 in written form?
zero and four hundred nineteen
four hundred nineteen hundredths
four hundred nineteen thousandts
A
B
C
D four one nine
24 What is 0.09 in written form?
nine and nine
nine hundredths
nine and nine hundredths
A
B
C
D nine and zero nine tenths
25 What is 407.021 in written form?
four zero seven zero two one
nine and nine tenths
four hundred seven and twenty one thousandths
A
B
C
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
tho
usa
nd
s
hu
nd
red
s
ten
s
on
es
and
ten
ths
hu
nd
red
ths
tho
usa
nd
ths
26 What is fifty two and eighteen hundredths?
52,18
52.01852.18
A
B
C
D 52.0018
27 What is five thousand fifty and five hundredths?
550.5
5,050.5
5,050.05
A
B
C
D 5,500.05
28 What is six hundred three and four thousandths?
603.4
603.004
603.04
A
B
C
D 603.0004
29 What is thirty four hundredths?
340
34
0.34
A
B
C
D 0.034
30 What is four hundred ninety five thousandths?
495
495.000
0.0495
A
B
C
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
>
<
=
greater than/largest
less than/ smallest
equal
SYMBOL WORDS
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
0.0450.210
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
put zero on the
end
Compare left to right. 2 is greater than 0, so 0.21 is
greatest.
0.045 < 0.21Click
0.3600.312
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
Compare left to right. 6 is greater than 1, so 0.36 is greatest.
0.36 > 0.312Click
0.0090.020
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
put zero on the
end
Compare left to right. 2 is greater than 0, so 0.02 is greatest.
0.009 < 0.02Click
Decimal Squares Interactive GamesClick 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.
0.41 0.049>
<
=
A
B
C
32 Choose the correct symbol.
0.301 0.311>
<
=
A
B
C
33 Choose the correct symbol.
0.007 0.05>
<
=
A
B
C
34 Choose the correct symbol.
0.179 0.24>
<
=
A
B
C
35 Choose the correct symbol.
0.46 0.6>
<
=
A
B
C
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:
910.800085.007910.801911.900085.070
What digit tells us this is the largest number?
1
Why isthis the smallest number?
Compare the digitsClick
×
36 The number with the least value is:
61.005
61.3
61.05
A
B
C
D 61.04
37 The number with the least value is:
0.005
0.5
0.05
A
B
C
D 0.0005
38 The number with the greatest value is:
9.888
9.8
9.008
A
B
C
D 9.088
39 The number with the greatest value is:
0.67
0.067
0.0067
A
B
C
D 0.00067
40 How much money would you like to win?
$150.59
$140.99
$150.82
A
B
C
D $140.50
Rewrite the numbers to order them from least to greatest.
15, 0, 1.5, 0.015, 0.15
0.709, 0.009, 0.68, 0.08, 0.07
Rewrite the numbers to order them from least to greatest.
41 Which of the following is ordered least to greatest?
0.3, 0.03, 0.33, 3.3
0.03, 0.3, 0.33, 3.3
3.3, 0.33, 0.3, 0.03
A
B
C
42 Which of the following is ordered least to greatest?
0.008, 0.06, 0.5
0.5, 0.06, 0.008
0.06, 0.5, 0.008
A
B
C
43 Which of the following is ordered greatest to least?
8.07, 0.008, 0.087, 0.87
0.008, 0.087, 0.87, 8.07
8.07, 0.87, 0.087, 0.008
A
B
C
44 Which of the following is ordered greatest to least?
0.23, 0.08, 0.009
0.23, 0.009, 0.08
0.009, 0.08, 0.23
A
B
C
45 Which of the following is ordered least to greatest?
0.8, 0.32, 0.41, 0.701
0.8, 0.701, 0.41, 0.32
0.32, 0.41, 0.701, 0.8
A
B
C
Round Numbers to Designated Place
ValuesReturn 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.
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.
Round 8,749 to the nearest ten.Review
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.
Round 8,749 to the nearest hundred.Review
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.
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
Rounding Decimals
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.
687.268
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.
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).
Round 8.73258 to the hundredths place.
Try this:Round 687.4953 to the nearest hundredths place
Answer: 687.50click
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.
When rounding to a specific place, your answer MUST have a digit in that place.
Example:Round 23.97 to the nearest tenth
Answer: 24.0There must be a digit in the tenths place, since we were to round to the tenths place.
Caution!
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 Estimate$5.99 $6$3.85 $4$1.29 $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 $2.99pencils $2.20book bag $15.75
68 Round the following items to the nearest dollar to figure out the approximate cost if all the items were bought.
jeans $24.99t-shirt $6.79hat $12.31
69 Round the following items to the nearest dollar to figure out the approximate cost if all the items were bought.
milk $3.79bread $2.15juice $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 $8.60potatoes $2.45peas $0.99
71 Round the following items to the nearest half dollar to figure out the cost if all the items were bought.
apples $4.60bananas $1.90oranges $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 $36.21sweatshirt $13.99socks $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 $688.23printer $213.50desk $175.89
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