Download Compare and Order Decimals

Name
1.4
?
Number and
Operations—5.2.B
MATHEMATICAL PROCESSES
5.1.A, 5.1.E
Compare and Order Decimals
Essential Question
How can you use place value to compare and order decimals?
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the Problem
Problem
The table lists some of the mountains in the United States
that are over two miles high. How does the height of Cloud
Peak in Wyoming compare to the height of Boundary
Peak in Nevada?
One Way Use place value.
Mountain Heights
Mountain and State
Height (in miles)
Boundary Peak, Nevada
2.488
Cloud Peak, Wyoming
2.495
Grand Teton Peak, Wyoming
2.607
Wheeler Peak, New Mexico
Line up the decimal points. Start at the left. Compare the
digits in each place-value position until the digits are different.
STEP 1 Compare the ones.
STEP 2 Compare the tenths.
2.495
2.495
●
Since 9 ● 8, then 2.495 ● 2.488, and 2.488 ● 2.495.
↓
↓
2=2
2.488
2.488
4
4
2.493
STEP 3 Compare the hundredths.
2.495
↓
2.488
9
●
8
So, the height of Cloud Peak is ___
the height of Boundary Peak.
Another Way Use a place-value chart to compare.
Compare the height of Cloud Peak to Wheeler Peak.
Ones
2
2
.
.
.
2=2
© Houghton Mifflin Harcourt Publishing Company
Since 5
●
Tenths
Hundredths
Thousandths
4
9
5
4
9
3
4=_
3, then 2.495
9=_
●
5>_
2.493, and 2.493
●
2.495.
So, the height of Cloud Peak is ___
the height of Wheeler Peak.
Math Talk
Mathematical Processes
Explain why it is important
to line up the decimal
points when comparing
decimals.
Module 1
23
Order Decimals You can use place value to order decimal numbers.
Example
Mount Whitney in California is 2.745 miles high, Mount Rainier in Washington
is 2.729 miles high, and Mount Harvard in Colorado is 2.731 miles high. Order
the heights of these mountains from least to greatest. Which mountain has the
least height? Which mountain has the greatest height?
STEP 1
STEP 2
Line up the decimal points. There
are the same number of ones.
Circle the tenths and compare.
Underline the hundredths and compare. Order from
least to greatest.
2.745
Whitney
2.729
Rainier
2.731
Harvard
There are the same number of
tenths.
2.745
Whitney
2.729
Rainier
2.731
Harvard
Since
● ● ●
<
<
, the heights in order from least to
greatest are __ , __ , __.
So, _____ has the least height and
Math Talk
_____ has the greatest height.
Mathematical Processes
Explain why you do not
have to compare the digits
in the thousandths place
to order the heights of
the 3 mountains.
Share
Share and
and Show
Show
numbers. What is the greatest place-value
position where the digits differ?
Ones
3
3
Compare. Write <, >, or =.
2. 4.563
● 4.536
3. 5.640
.
.
Tenths
Hundredths
Thousandths
4
7
2
4
4
5
● 5.64
4. 8.673
● 8.637
Name the greatest place-value position where the
digits differ. Name the greater number.
5. 3.579; 3.564
____
____
24
6. 9.572; 9.637
____
____
7. 4.159; 4.152
____
____
© Houghton Mifflin Harcourt Publishing Company
1. Use the place-value chart to compare the two
Name
Problem
Problem Solving
Solving
Order from greatest to least.
8. 2.007; 2.714; 2.09; 2.97
9. 0.386; 0.3; 0.683; 0.836
______
______
Algebra Find the unknown digit to make each statement true.
10. 3.59 > 3.5
1 > 3.572
11. 6.837 > 6.83
> 6.835
12. 2.45 < 2.
6 < 2.461
13. Dawn keeps track of her softball batting average each year. The first
year, her batting average is .783. The second year, her batting average
is .81. In which year did she have the greater batting average?
Problem
Problem Solving
Solving
Use the table for 14–16.
Mountains Over Three Miles High
14. Use Math Language How does the height of Steele
Mountain and Location
© Houghton Mifflin Harcourt Publishing Company
Mountain compare to the height of Blackburn Mountain?
Compare the heights using words.
Height (in miles)
Blackburn, Alaska
3.104
Bona, Alaska
3.134
Steele, Yukon
3.152
15.
Write Math
Explain how to order the height of the mountains
from greatest to least.
16.
Multi-Step What if the height of Blackburn Mountain
were 0.05 mile greater. Would it then be the mountain with the
greatest height? Explain.
Module 1 • Lesson 4
25
Mathematical Processes
M
Model ¥ Reason ¥ Communicate
M
Daily
Daily Assessment
Assessment Task
Task
Fill in the bubble completely to show your answer.
17. The length of a piece of plastic for a science kit needs to be greater
than 22.4 inches and less than 22.5 inches. Which length of plastic
can be used?
A
22.35 in
C
22.47 in.
B
22.51 in
D
22.40 in.
18. Louis is comparing the numbers 8.402 and 8.451. What is the least place
value he needs to compare to decide which number is greater?
A
ones
B
tenths
C
hundredths
D
thousandths
19. Multi-Step Melinda compares four numbers. Which shows the
numbers from least to greatest?
A
3.04; 3.10; 3.529; 3.685
B
3.10; 3.04; 3.529; 3.685
C
3.10; 3.04; 3.685; 3.529
D
3.04; 3.685; 3.529; 3.10
TEXAS Test Prep
20. Mount Logan in the Yukon is 3.702 miles high. Mount McKinley in
26
A
Logan, McKinley, Pico de Orizaba
B
McKinley, Logan, Pico de Orizaba
C
Pico de Orizaba, Logan, McKinley
D
Logan, Pico de Orizaba, McKinley
© Houghton Mifflin Harcourt Publishing Company
Alaska is 3.848 miles high and Pico de Orizaba in Mexico is 3.571 miles
high. Order these mountains by height from greatest to least.
Number and Operations—5.2.B
MATHEMATICAL PROCESSES 5.1.A, 5.1.E
H o mewo rk
and Practice
1.4
Name
Compare and Order Decimals
Compare. Write <, >, or =.
1. 9.23
● 9.32
2. 7.20
● 7.2
3. 1.994
4. 4.44
● 4.044
5. 3.61
● 3.87
6. 5.4
● 1.493
● 5.400
Order from greatest to least.
8. 1.001; 1.1; 1.403; 1.078
7. 7.081; 7.81; 7.002; 7.14
10. 4; 4.022; 4.002; 4.221
9. 0.04; 0.5; 0.021; 0.133
Problem
Problem Solving
Solving
Find the unknown digit to make each statement true.
11. 5.345 > 5.34
> 5.343
12. 8.25 < 8.
14. Jack travels 2.45 miles to school. Wanda travels
© Houghton Mifflin Harcourt Publishing Company
2.31 miles to school. Compare the distances
using words.
6 < 8.361
13. 6.48 > 6.4
1 > 6.470
15. In a jumping contest, Marcus jumped
1.02 meters, Gustavo jumped 1.29 meters, and
Loreena jumped 1.202 meters. Who won the
jumping contest?
Module 1 • Lesson 4
27
TEXAS Test Prep
Lesson
Lesson Check
Check
Fill in the bubble completely to show your answer.
16. Which number has the greatest value?
A
9.382
B
9.47
9.210. What is the least place value she
needs to compare to decide which
number is greater?
C
9.09
A
ones
D
9.7
B
thousandths
C
hundredths
D
tenths
18. Which number has the least value?
7.034
B
7.304
C
7.403
D
7.003
19. In 5.820, what is the place-value position
of the 0?
her pet fish. The table shows the lengths of the
fish. Which shows the lengths in order from
greatest to least?
A
thousandths
B
tenths
C
hundredths
D
ones
21. Multi-Step Look at the table in Question 20.
What if Gem grew 0.5 inches. Which would
then show the lengths in order from
greatest to least?
Name
Length
A
Gem, Spots, Gus, Oscar
Oscar
4.32 inches
B
Gus, Oscar, Gem, Spots
Gus
4.055 inches
4.21 inches
C
Gem, Spots, Oscar, Gus
Gem
Spots
4.7 inches
D
Spots, Oscar, Gem, Gus
A
Spots, Oscar, Gus, Gem
B
Oscar, Spots, Gem, Gus
C
Gus, Oscar, Gem, Spots
D
Spots, Oscar, Gem, Gus
© Houghton Mifflin Harcourt Publishing Company
A
20. Multi-Step Jenna compares the lengths of
28
17. Kerry is comparing the numbers 9.207 and