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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? Unlock Unlock the 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