Download Place Value of Decimals

Name
1.3
?
Number and
Operations—5.2.A
Also 5.2.B
MATHEMATICAL PROCESSES
5.1.D
Place Value of Decimals
Essential Question
How do you read, write, and represent decimals
through thousandths?
Unlock
Unlock the
the Problem
Problem
The Brooklyn Battery Tunnel in New York City is 1.726 miles
long. It is the longest underwater tunnel for vehicles in
the United States. To understand this distance, you need
to understand the place value of each digit in 1.726.
You can use a place-value chart to understand decimals.
Whole numbers are to the left of the decimal point. Decimals
are to the right of the decimal point. The thousandths place
is to the right of the hundredths place.
Tens
Ones
1
•
Tenths
Hundredths
Thousandths
7
2
6
1×1
1
7 × __
1
2 × ___
1
6 × _____
1.0
0.7
0.02
0.006
10
100
1,000
▲ The Brooklyn Battery Tunnel passes
under the East River.
} Value
The place value of the digit 6 in 1.726 is thousandths. The value of 6
1 , or 0.006.
in 1.726 is 6 _____
Math Talk
1,000
© Houghton Mifflin Harcourt Publishing Company • Image Credits: (tr) ©Jeremy Graham/Alamy Images
Standard Form: 1.726
Word Form: one and seven hundred twenty-six thousandths
Mathematical Processes
Explain how the value of the
last digit in a decimal can
help you read a decimal.
Expanded Form: 1 + 0.7 + 0.02 + 0.006
Try This! Use place value to read and write decimals.
A Standard Form: 2.35
Word Form: two and _____
Expanded Form: 2 + _____
B Standard Form: __
Word Form: three and six hundred fourteen thousandths
Expanded Form: __ + 0.6 + __ + __
Module 1
17
Example Use place value to compare.
The silk spun by a common garden spider is about 0.003 millimeter thick.
A commonly used sewing thread is about 0.3 millimeter thick. How does
the thickness of the spider silk and the thread compare?
Count the number of decimal place-value positions to the digit 3 in
0.3 and 0.003.
0.3 has _ fewer decimal places than 0.003
2 fewer decimal places: 10 × 10 = __
0.3 is __ times as much as 0.003
0.003 is __ of 0.3
So, the thread is __ times as thick as the garden spider’s silk.
The thickness of the garden spider’s silk is
__ that of the thread.
Share
Share and
and Show
Show
1. Complete the place-value chart to find the value of each digit.
Ones
3
•
Tenths
Hundredths
Thousandths
5
2
4
1
2 × ___
3×1
} Value
100
0.5
Write the value of the underlined digit.
2. 0.543
3. 6.234
____
4. 3.954
____
____
5. 0.253
______
______
______
18
6. 7.632
______
______
______
© Houghton Mifflin Harcourt Publishing Company
Write the number in two other forms.
Name
Problem
Problem Solving
Solving
7. Connect You can use place-value patterns
to rename a decimal. Complete the chart
to rename 0.3 using other place values.
8.
Write Math
Explain how you know that
the digit 6 in the numbers 3.675 and 3.756 does
not have the same value.
0.300
3 tenths
1
3 × __
0.300
_ hundredths
_ × 100
0.300
10
1
___
___ ___
Problem
Problem Solving
Solving
Use the table for 9–11.
9. What is the value of the digit 7 in New Mexico’s
average annual rainfall?
10. The average annual rainfall in Maine is one and
seventy-four thousandths meters per year. Complete
the table by writing that amount in standard form.
Average Annual Rainfall (in meters)
California
0.564
New Mexico
0.372
New York
1.041
Wisconsin
0.820
Maine
11. Which of the states has an average annual rainfall
with the least number in the thousandths place?
© Houghton Mifflin Harcourt Publishing Company
Write Math
12.
Multi-Step Dan used a meter stick to
measure some seedlings in his garden. One day, a
corn stalk was 0.85 m tall. A tomato plant was 0.850 m.
A carrot top was 0.085 m. Which plant was shortest?
13.
What’s the Error? Damian wrote the number four
and twenty-three thousandths as 4.23. Describe and correct his error.
Show Your Work
Module 1 • Lesson 3
19
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
14. Although the average turkey sandwich in Turkeyton costs 3.456
dollhorts, the cost of a gourmet turkey sandwich at Sandwich Palace
is 5.032 dollhorts. What does the 3 in 5.032 dollhorts represent?
A
3 dollhorts
B
3 tenths of a dollhort
C
3 hundredths of a dollhort
D
4 hundredths of a dollhort
15. Use Math Language One meter is equal to about 3.281 feet. What is
the word form of this decimal?
A
three and twenty-eight hundredths and one thousandth
B
three and two hundred eighty-one thousandths
C
three and two tenths and eighty-one thousandths
D
three point two eighty-one
16. Multi-Step Sam had a piece of ribbon 8.469 centimeters long. He cut
off exactly one tenth of a centimeter from the ribbon. Then he cut off two
hundredths of a centimeter. How long is the ribbon now?
A
8.169 cm
B
8.269 cm
C
8.349 cm
D
8.466 cm
TEXAS Test Prep
20
A
4
B
7
C
3
D
6
© Houghton Mifflin Harcourt Publishing Company
17. In 24.736, which digit is in the thousandths place?
Number and Operations—5.2.A,
5.2.B
MATHEMATICAL PROCESSES 5.1.D
H o mewo rk
and Practice
1.3
Name
Place Value of Decimals
Rename 0.6 using other place values.
1.
0.600
6 tenths
1
6 × __
10
0.600
_ hundredths
1
_ × ___
100
0.600
Rename 0.2 using other place values.
2.
0.200
2 tenths
1
2 × __
10
0.200
20 __
20 × _
0.200
Write the number in two other forms.
3. 0.632
4. 4.293
Problem
Problem Solving
Solving
© Houghton Mifflin Harcourt Publishing Company
5. A weather reporter reads aloud the number of
meters of snowfall. The amount is 0.103 meter.
What words should the reporter use on the air
to explain the amount of snowfall?
6. Amil says that the snow on the ground is
1 meter high. How can this number be
5 × ___
100
expressed as a decimal?
Module 1 • Lesson 3 21
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
thousandths place?
1 ?
7 × ____
1,000
A
5
A
0.7
B
9
B
0.007
C
2
C
0.07
D
3
D
7.0
9. Multi-Step Which value correctly represents
the number that is 10 times as great as five
hundred eighty-one thousandths?
A
5.81
B
581
C
0.581
D
500.81
11. Jack’s baby sister crawled three and five tenths
meters today. Which number represents that
distance?
22
8. Which number has the same value as
10. Which number has the same value
1?
as 3 × __
10
A
0.003
B
3.10
C
0.3
D
0.03
12. Multi-Step Leon measured the distance
each of his four toy cars rolled across the floor.
Which car measurement that has a 4 in the
thousandths place represents the shortest
distance rolled?
A
3.5
B
3.05
A
0.741 meter
C
3.510
B
0.714 meter
D
3.005
C
0.224 meter
D
0.213 meter
© Houghton Mifflin Harcourt Publishing Company
7. In the number 5.923, which number is in the