Compare and Order Decimals 5.1.A, 5.1.E ? Essential Question How Can You Use Place Value to Compare and Order Decimals?

Home , Mount Logan, Wheeler Peak (Nevada)

Name Number and Operations—5.2.B 1.4 MATHEMATICAL PROCESSES Compare and Order Decimals 5.1.A, 5.1.E ? Essential Question How can you use place value to compare and order decimals?

UnlockUnlock thethe ProblemProblem

The table lists some of the mountains in the United States Mountain Heights that are over two miles high. How does the height of Cloud Mountain and State Height (in miles) Peak in Wyoming compare to the height of Boundary Peak in Nevada? Boundary Peak, Nevada 2.488 Cloud Peak, Wyoming 2.495 One Way Use place value. Grand Teton Peak, Wyoming 2.607 Line up the decimal points. Start at the left. Compare the Wheeler Peak, New Mexico 2.493 digits in each place-value position until the digits are different.

STEP 1 Compare the ones. STEP 2 Compare the tenths. STEP 3 Compare the hundredths.

2.495 2.495 2.495

↓ 2 = 2 ↓ 4 ● 4 ↓ 9 ● 8 2.488 2.488 2.488

Since 9 ● 8, then 2.495 ● 2.488, and 2.488 ● 2.495.

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. Tenths Hundredths Thousandths 24. 9 5 24. 9 3

2 = 24 = _ 9 = _ 5 > _

Math Talk Since 5 ● 3, then 2.495 ● 2.493, and 2.493 ● 2.495. Mathematical Processes

Explain why it is important So, the height of Cloud Peak is ___ to line up the decimal points when comparing the height of Wheeler Peak. decimals.

Module 1 23 © Houghton Mifflin Harcourt Publishing Company 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 Underline the hundredths and compare. Order from are the same number of ones. least to greatest. Circle the tenths and compare. 2.745 Whitney 2.745 Whitney 2.729 Rainier 2.729 Rainier 2.731 Harvard 2.731 Harvard Since ● < ● < ●, the heights in order from least to There are the same number of tenths. 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. ShareShare andand ShowShow

1. Use the place-value chart to compare the two Ones Tenths Hundredths Thousandths numbers. What is the greatest place-value 34. 7 2 position where the digits differ? 34. 4 5

Compare. Write <, >, or =.

2. 4.563 ● 4.536 3. 5.640 ● 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 6. 9.572; 9.637 7. 4.159; 4.152 ______

24 © Houghton Mifflin Harcourt Publishing Company Name

ProblemProblem SolvingSolving

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?

ProblemProblem SolvingSolving

Use the table for 14–16. Mountains Over Three Miles High 14. Use Math Language How does the height of Steele Mountain and Location Height (in miles) Mountain compare to the height of Blackburn Mountain? Blackburn, Alaska 3.104 Compare the heights using words. 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 © Houghton Mifflin Harcourt Publishing Company MathematicalM Processes MModel ¥ Reason ¥ Communicate DailyDaily AssessmentAssessment TaskTask

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 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.

A Logan, McKinley, Pico de Orizaba

B McKinley, Logan, Pico de Orizaba

C Pico de Orizaba, Logan, McKinley

D Logan, Pico de Orizaba, McKinley

26 © Houghton Mifflin Harcourt Publishing Company Number and Operations—5.2.B Homework MATHEMATICAL PROCESSES 5.1.A, 5.1.E and Practice Name

1.4 Compare and Order Decimals

Compare. Write <, >, or =.

1. 9.23 ● 9.32 2. 7.20 ● 7.2 3. 1.994 ● 1.493

4. 4.44 ● 4.044 5. 3.61 ● 3.87 6. 5.4 ● 5.400

Order from greatest to least.

7. 7.081; 7.81; 7.002; 7.14 8. 1.001; 1.1; 1.403; 1.078

9. 0.04; 0.5; 0.021; 0.133 10. 4; 4.022; 4.002; 4.221

ProblemProblem SolvingSolving

Find the unknown digit to make each statement true.

11. 5.345 > 5.34 > 5.343 12. 8.25 < 8. 6 < 8.361 13. 6.48 > 6.4 1 > 6.470

14. Jack travels 2.45 miles to school. Wanda travels 15. In a jumping contest, Marcus jumped 2.31 miles to school. Compare the distances 1.02 meters, Gustavo jumped 1.29 meters, and using words. Loreena jumped 1.202 meters. Who won the jumping contest?

Fill in the bubble completely to show your answer.

16. Which number has the greatest value? 17. Kerry is comparing the numbers 9.207 and 9.210. What is the least place value she A 9.382 needs to compare to decide which B 9.47 number is greater?

C 9.09 A ones

D 9.7 B thousandths C hundredths

D tenths

18. Which number has the least value? 19. In 5.820, what is the place-value position of the 0? A 7.034 A thousandths B 7.304 B tenths C 7.403 C hundredths D 7.003 D ones

20. Multi-Step Jenna compares the lengths of 21. Multi-Step Look at the table in Question 20. her pet fish. The table shows the lengths of the What if Gem grew 0.5 inches. Which would fish. Which shows the lengths in order from then show the lengths in order from greatest to least? greatest to least?

Name Length A Gem, Spots, Gus, Oscar Oscar 4.32 inches B Gus, Oscar, Gem, Spots Gus 4.055 inches C Gem, Spots, Oscar, Gus Gem 4.21 inches 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