G5 Go Math Place Value and Decimals PDF

Chapter Name 4 Place Value and Decimals Show What You Know...

Chapter Name 4 Place Value and Decimals Show What You Know Place Value and Whole Numbers Write the value of the digit. 1. 1,342 2. 2,187 The value of 3 is ___. The value of 2 is ___. Decimals Greater Than One Write the word form and the expanded form for each. 3. 3.4 4. 2.51 Relate Fractions and Decimals Write as a decimal or a fraction. 5. 0.8 _ ​  5 ​ 6. ___ 100 _ 7. 0.46 _ ​  6 ​ 8. __ 10 _ 9. 0.90 __ ​  35 ​ 10. ___ 100 _ © Houghton Mifflin Harcourt Publishing Company Image Credit: ©HMH l MATH in the Reoarld W Jason has 4 tiles. Each tile has a number printed on it. The numbers are 2, 3, 6, and 8. A decimal number is formed using the tiles and the clues. Find the number. Chapter 4 119  Vocabulary Builder Go Online For more help Visualize It Connect to Vocabulary Use the ✓ words to complete the tree map. Review Words ✓ benchmark ✓ hundredth Estimation ✓ place value ✓ round ✓ tenth Preview Words ✓ thousandth Understand Vocabulary Read the description. Which word do you think is described? 1. One of one hundred equal parts ___ 2. The value of each digit in a number based on the location of the digit ___ 3. To replace a number with one that is simpler and is approximately © Houghton Mifflin Harcourt Publishing Company Image Credit: ©HMH the same size as the original number ___ 4. One of ten equal parts ___ 5. A familiar number used as a point of reference ___ 6. One of one thousand equal parts ___ 120  Go Math! Grade 5  CHAPTER 4 Name Lesson 1 Understand Thousandths I Can describe the relationship between two decimal place-value positions. Investigate Materials color pencils straightedge Thousandths are smaller parts than hundredths. If one hundredth is divided into ten equal parts, each part is one thousandth. Use the model at the right to show tenths, hundredths, and thousandths. A. Divide the larger square into 10 equal columns or rectangles. Shade one rectangle. What part of the whole is the shaded rectangle? Write that part as a decimal and a fraction. B. Divide each rectangle into 10 equal squares. Use a second color to shade in one of the squares. What part of the whole is the shaded square? Write that part as a decimal and a fraction. C. Divide the enlarged hundredths square into 10 equal columns or rectangles. If each hundredths square is divided into ten equal rectangles, how many parts will the model have? © Houghton Mifflin Harcourt Publishing Company Image Credit: ©HMH Use a third color to shade one rectangle of the enlarged hundredths square. What part of the whole is the shaded rectangle? Write that part as a decimal and a fraction. _________ Math Construct arguments and Talk MP critique reasoning of others. There are 10 times as many hundredths as there are tenths. Explain how the model shows this. Chapter 4 Lesson 1   121 Draw Conclusions 1. Explain what each shaded part of your model in the Investigate section shows. What fraction can you write that relates each shaded part to the next greater shaded part? 2. MP Identify and describe a part of your model that shows one thousandth. Explain how you know. Make Connections The relationship of a digit in different place-value positions is the same with decimals as it is with whole numbers. You can use your understanding of place-value patterns and a place-value chart to write decimals that are 10 times as much as or ​ __ 1 10 ​ of a decimal. Ones Tenths Hundredths Thousandths 0 0 4 ? 0.04 ? __ is 10 times as much as 0.04. 10 times 1 of __ is ___ ​ 1 ​of 0.04. 10 as much 10 Use the steps below to complete the table. STEP 1 Write the given decimal in a 10 times 1 ​ of place-value chart. Decimal ​ __ as much as 10 STEP 2 Use the place-value chart to write a 0.03 decimal that is 10 times as much as the given decimal. 0.1 © Houghton Mifflin Harcourt Publishing Company STEP 3 Use the place-value chart to write a 0.07 decimal that is ​ __ 10 1  ​of the given decimal. Math Look for and make use Talk MP of structure. Explain the pattern you see when you move one decimal place value to the right and one decimal place value to the left. 122 Go Math! Grade 5  Name Share and Show Math Board Write the decimal shown by the shaded parts of each model. 1. 2. __ __ 3. 4. __ __ Complete the sentence. 5. 0.6 is 10 times as much as __. ​ 1 ​of __. 6. 0.007 is __ 10 1 ​of __. 7. 0.008 is ​ __ 10 8. 0.5 is 10 times as much as __. Use place-value patterns to complete the table. 10 times 1 ​ of 10 times 1 ​ of Decimal ​ __ Decimal ​ __ as much as 10 as much as 10 9. 0.2 13. 0.06 © Houghton Mifflin Harcourt Publishing Company 10. 0.07 14. 0.9 11. 0.05 15. 0.3 12. 0.4 16.   0.08 Chapter 4 Lesson 1   123  Problem Solving · Applications Real World Use the table for Problems 17 and 18. 17. A science teacher showed an image of a carpenter bee on a wall. The image is 10 times as large as the actual bee. Then he showed another image of the bee that is Bee Lengths (in meters) 10 times as large as the first image. What is the length Bumblebee 0.019 of the bee in the second image? Carpenter Bee 0.025 Leafcutting Bee 0.014 18. An atlas beetle is about 0.14 meter long. Orchid Bee 0.028 How does the length of the atlas beetle Sweat Bee 0.006 on the compare to the length of a leafcutting Spot bee? Show the Math Demonstrate Your Thinking 19. Write Math Explain how you can use place value to describe how 0.05 and 0.005 compare. 20. MP Terry, Sasha, and Harry each choose a number. © Houghton Mifflin Harcourt Publishing Company Image Credits: (tr) ©Photodisc/Getty Images Terry’s number is ten times as much as Sasha’s. Harry’s ​ 1 ​of Sasha’s. Sasha’s number is 0.4. What number is __ 10 number did each person choose? 21. Choose the numbers that make the statement true. 0.065 ​  ​ 0.065 0.65 is 10 times as much as 0.65 1 of and __ 0.65. 10 6.5 6.5 65.0 65.0 124 Go Math! Grade 5  LESSON 4.1 Name Practice and Homework Understand Thousandths Write the decimal shown by the shaded parts of each model. 1. 2. 0.236 Think: 2 tenths, 3 hundredths, and 6 thousandths are shaded Complete the sentence. 3. 0.4 is 10 times as much as __. 4. 0.003 is ​ __ 1 10 ​of __. Use place-value patterns to complete the table. 10 times as 1 ​of 10 times as 1 ​of Decimal ​  ___ Decimal ​  ___ 10 much as 10 much as 5. 0.1 7. 0.08 6. 0.09 8. 0.2 Problem Solving Real World 9. The diameter of a dime is seven hundred five U.S. Coins thousandths of an inch. Complete the table Coin Diameter (in inches) by recording the diameter of a dime. Penny 0.750 10. What is the value of the 5 in the diameter of a half dollar? Nickel 0.835 Dime 11. Which coins have a diameter with a 5 in the Quarter 0.955 © Houghton Mifflin Harcourt Publishing Company hundredths place? Half dollar 1.205 12. Write Math Write four decimals with the digit 4 in a different place in each—ones, tenths, hundredths, and thousandths. Then write a statement that compares the value of the digit 4 in the different decimals. Chapter 4 Lesson 1   125 Lesson Check ​ 1 ​of 3.0. 13. Write a decimal that is __ 14. A penny is 0.061 inch thick. What is the value of 10 the 6 in the thickness of a penny? Spiral Review 15. What is the number seven hundred thirty-one 16. A city has a population of 743,182 people. million, nine hundred thirty-four thousand, What is the value of the digit 3? thirty written in standard form? 17. Identify the property that the equation shows. 18. Mars is about 190,000,000 miles from the Earth. What is this distance written as a whole number 3×(8×4)=(3×8)×4 multiplied by a power of 10? © Houghton Mifflin Harcourt Publishing Company 126  Go Math! Grade 5  CHAPTER 4 Name Lesson 2 Read and Write Decimals Through Thousandths I Can read, write, and represent decimals through thousandths. UNLOCK the Problem Real World 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 ▲ The Brooklyn Battery Tunnel passes to the right of the hundredths place. under the East River. Tens Ones Tenths Hundredths Thousandths 1 7 2 6 ​  1 ​ ​  1 ​ ​  1 ​ 1×1 1.0 7 × __ 0.7 10 2 × ___ 100 0.02 6 × _____ 1,000 0.006 } Value The place value of the digit 6 in 1.726 is thousandths. The value ____ 1  ​ , or 0.006. of 6 in 1.726 is 6 × ​  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 Math Look for and make use Talk MP of structure. Expanded Form: 1 × 1 + 7 × ​  ​ __ ( 10 ) ( 100 ) 1 ​  ​ + 2 × ​  ​ ___ ( 1,000 ) 1 ​  ​ + 6 × ​  ​ _____ 1 ​  ​ Explain how the place value of the last digit in a decimal can help you read a decimal. Try This! Use place value to read and write decimals. A  Standard Form: 2.35 Word Form: two and _____ Expanded Form: 2 × 1+ _____ B  Standard Form: __ Word Form: three and six hundred fourteen thousandths Expanded Form: __ + 6 × ​  ​ __ 1 ​  ​ + __ + __ ( 10 ) Chapter 4 Lesson 2   127  Example Use a place-value chart. A common garden spider spins a web with its silk that 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? STEP 1 Write the numbers in a place-value chart. Ones Tenths Hundredths Thousandths STEP 2 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 © Houghton Mifflin Harcourt Publishing Company Image Credits: (tr) ©Comstock Images/Getty Images __ that of the thread. You can use place-value patterns to rename a decimal. Try This! Use place-value patterns. Rename 0.3 using other place values. 0.300 3 tenths 1​ 3 × ​ __ 10 ​  ​ 1 ___ 0.300 _ hundredths _ × 100 0.300 ___ ___ 128 Go Math! Grade 5  Name Share and Show Math Board 1. Complete the place-value chart to find the value of each digit. Ones Tenths Hundredths Thousandths 3 5 2 4 ​  1 ​ 3×1 2 × ___ 100 } Value 0.5 Write the value of the underlined digit. 2. 0.543 3. 6.234 4. 3.954 Write the number in two other forms. 5. two hundred fifty-three thousandths 6. 7.632 On Your Own Write the value of the underlined digit. 7. 0.496 8. 2.726 9. 1.066 10. 6.399 11. 0.002 12. 14.371 © Houghton Mifflin Harcourt Publishing Company Write the number in two other forms. 13. four hundred eighty nine thousandths 14. 5.916 Chapter 4 Lesson 2   129  Problem Solving · Applications Real World Use the table for problems 15–16. Average Annual Rainfall (in meters) 15. What is the value of the digit 7 in New Mexico’s average annual rainfall? California 0.564 New Mexico 0.372 New York 1.041 16. Which of the states has an average annual Wisconsin 0.820 rainfall with the least number in the Maine 1.074 thousandths place? What is another way to write the total annual rainfall in this state? Show the Math Demonstrate Your Thinking 17. MP Damian wrote the number four and twenty-three thousandths as 4.23. Describe and correct his error. 18. Dan used a meter stick to measure some seedlings in his garden. One day, a corn stalk was 0.85 m on the tall. A tomato plant was 0.850 m. A carrot top was Spot 0.085 m. Which plant was shortest? 19. Write Math Explain how you know that the digit 6 does not have the same value in the numbers 3.675 and 3.756. © Houghton Mifflin Harcourt Publishing Company 20. What is the value of the underlined digit? Mark all that apply. 0.589 0.8 eight hundredths 0.08 1 ​) 8 × (​ __ 10 eight tenths 130 Go Math! Grade 5  LESSON 4.2 Name Practice and Homework Read and Write Decimals Through Thousandths Write the value of the underlined digit. 1. 0.287 2. 5.349 3. 2.704 8 hundredths, or 0.08 4. 9.154 5. 4.006 6. 7.258 Write the number in two other forms. 1 ​) + 2 ∙ (​ ___ 7. 3 ∙ (​ __ 1 ​) + 6 ∙ (​ _____ 1 ​) 8. 8.517 10 100 1,000 9. nine hundred twenty-four thousandths 10. 1.075 Problem Solving Real World 11. In a gymnastics competition, Paige’s score was 12. Haru’s batting average for the softball season is 37.025. What is Paige’s score written in word 0.368. What is Haru’s batting average written in © Houghton Mifflin Harcourt Publishing Company form? expanded form? 13. Write Math Write five decimals that have at least 3 digits to the right of the decimal point. Write the expanded form and the word form for each number. Chapter 4 Lesson 2   131 Lesson Check 14. When Mindy went to China, she exchanged 15. The diameter of the head of a screw $1 for 6.589 Yuan. What digit is in the is 0.306 inch. What is this number written hundredths place of 6.589? in word form? Spiral Review 16. Each car on a commuter train can seat 17. Write a decimal that is ​ __ 1 10 ​of 6.0. 114 passengers. If the train has 7 cars, how many passengers can the train seat? 18. A quarter is 1.75 millimeters thick. What is the 19. There are 138 people seated at the tables in value of the 5 in the thickness of a quarter? a banquet hall. Each table can seat 12 people. All the tables are full except one. How many full tables are there? © Houghton Mifflin Harcourt Publishing Company 132  Go Math! Grade 5  CHAPTER 4 Name Lesson 3 Compose and Decompose Decimals I Can compose and decompose multi-digit numbers with decimals. Investigate Materials base-ten blocks You can use base-ten blocks to understand the relationships among decimal place-value positions. Use a large cube for 1, a flat for ​ __ 1 ___1 ____1 10 ​, a long for ​ 100 ​, and a small cube for ​ 1,000 ​. Number 1,000 100 10 1 Model large small Description flat long cube cube You can decompose numbers with decimals in different ways. A. Use the blocks to model 2.543. What did you use? Draw them and list the number of each. _ large cubes _ flats _ longs _ small cubes 2.543 = _ ones + _ tenths + _ hundredths + _ thousandths B. Replace 1 of the longs with small cubes. Record your results. _ large cubes _ flats _ longs _ small cubes © Houghton Mifflin Harcourt Publishing Company 2.543 = _ ones + _ tenths + _ hundredths + _ thousandths C. Now replace 2 of the flats with longs. Record your results. Math Look for and make use _ large cubes _ flats Talk MP of structure. _ longs _ small cubes How many times as much is the long compared to the small cube? the flat compared to the 2.543 = _ ones + _ tenths + _ hundredths + _ thousandths small cube? Explain. Chapter 4 Lesson 3   133 Draw Conclusions 1. MP Why can you replace a long with 10 small cubes? 2. MP How can you check to see if you decomposed the number correctly? Make Connections You can use your understanding of place-value patterns and a place-value chart to write and decompose decimal numbers. Use the steps below to show different ways to decompose the decimal. STEP 1 Build 4.598 with base ten blocks. Draw your blocks. 4.598 = _ ones + _ tenths + _ hundredths + _ thousandths STEP 2 Decompose three of the flats into longs. 4.598 = _ ones + _ tenths + _ hundredths + _ thousandths STEP 3 Now decompose 2 longs into small cubes. 4.598 = _ ones + _ tenths + _ hundredths + _ thousandths Ones Tenths Hundredths Thousandths 4 5 9 8 © Houghton Mifflin Harcourt Publishing Company 10 times 10 times 10 times as much as much as much as 134 Go Math! Grade 5  Name Share and Show Math Board Decompose the decimal number two different ways. 1. 4.763 = _ ones + _ tenths + _ hundredths + _ thousandths 4.763 = _ ones + _ tenths + _ hundredths + _ thousandths 2. 7.402 = _ ones + _ tenths + _ hundredths + _ thousandths 7.402 = _ ones + _ tenths + _ hundredths + _ thousandths 3. What number is composed of 5 ones, 17 tenths, 22 hundredths and 9 thousandths? _ On Your Own Decompose the decimal number two different ways. 4. 3.587 = _ ones + _ tenths + _ hundredths + _ thousandths 3.587 = _ ones + _ tenths + _ hundredths + _ thousandths 5. 1.296 = _ ones + _ tenths + _ hundredths + _ thousandths 1.296 = _ ones + _ tenths + _ hundredths + _ thousandths 6. 2.809 = _ ones + _ tenths + _ hundredths + _ thousandths 2.809 = _ ones + _ tenths + _ hundredths + _ thousandths 7. What number is composed of 8 ones, 35 tenths, 17 hundredths and 13 thousandths? _ 8. What number is composed of 4 ones, 21 tenths, 32 hundredths and 4 thousandths? _ 9. What number is composed of 8 ones, 11 tenths, 11 hundredths and 11 thousandths? © Houghton Mifflin Harcourt Publishing Company _ 10. Write Math Write a decimal number. How many ways can you decompose your number? 11. MP 0.3 is __ times as much as 0.003. 3 tenths = __ thousandths Chapter 4 Lesson 3   135 12. Joji and Goro use base-ten blocks to model 3.137. Whose model makes sense? Whose model does not make sense? Explain your reasoning. Joji’s Work Goro’s Work _ ones + _ tenths + _ ones + _ tenths + _ hundredths + _ thousandths _ hundredths + _ thousandths 13. Explain how Goro could make his model represent the number. 14. For Problems 14a–14c, choose True or False for each equation. 14a. 5.4 = 54 tenths True False 14b. 6.73 = 6 ones + 73 tenths True False 14c. 0.492 = 20 hundredths + 292 thousandths True False © Houghton Mifflin Harcourt Publishing Company 136 Go Math! Grade 5  LESSON 4.3 Name Practice and Homework Compose and Decompose Decimals Decompose the decimal number two different ways. 1. 5.924 = _ ones + _ tenths + _ hundredths + _ thousandths 5.924 = _ ones + _ tenths + _ hundredths + _ thousandths 2. 7.881 = _ ones + _ tenths + _ hundredths + _ thousandths 7.881 = _ ones + _ tenths + _ hundredths + _ thousandths 3. 3.465 = _ ones + _ tenths + _ hundredths + _ thousandths 3.465 = _ ones + _ tenths + _ hundredths + _ thousandths 4. What number is composed of 8 ones, 16 tenths, 24 hundredths and 37 thousandths? _ 5. What number is composed of 2 ones, 29 tenths, 17 hundredths and 105 thousandths? _ 6. What number is composed of 6 ones, 22 tenths, 33 hundredths and 44 thousandths? _ Problem Solving Real World 7. Earth is about 4.54 billion years old. 8. Franklin weighs his puppy in pounds. He Decompose 4.54 two different ways. decomposes the weight as shown. 8 ones + 13 tenths + 24 hundredths + 176 thousandths How much does his puppy weigh in pounds? © Houghton Mifflin Harcourt Publishing Company 9. Write Math How does place value help you decompose numbers in different ways? Chapter 4 Lesson 3   137 Lesson Check 10. Decompose 6.279. Choose all that apply. 11. What number is composed of 3 ones, 24 tenths, 55 hundredths and 117 thousandths? A  5 ones + 12 tenths + 4 hundredths + 39 thousandths B  6 ones + 1 tenth + 8 hundredths + 9 thousandths C  5 ones + 11 tenths + 7 hundredths + 19 thousandths D  6 ones + 3 hundredths + 249 thousandths Spiral Review 12. Write the decimal. 13. Divide. Write the remainder as a fraction. twenty-six and four hundred eighteen 85,723 ÷ 9 thousandths 14. Estimate the quotient. 15. Jeremy has 374 baseball cards. He keeps them in a book that holds 6 cards per page. How 5,572 ÷ 8 many pages in his book are full? How many cards are on the last page? © Houghton Mifflin Harcourt Publishing Company 138  Go Math! Grade 5  CHAPTER 4 Name Lesson 4 Compare and Order Decimals I Can use place value to compare and order decimals. UNLOCK the Problem Real World 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? Mountain Heights Mountain and State Height (in miles) Boundary Peak, Nevada 2.488 Cloud Peak, Wyoming 2.495 ▲ The Tetons are located in Grand Teton National Park. Grand Teton Peak, Wyoming 2.607 Wheeler Peak, New Mexico 2.493 One Way Use place value. 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. 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. © Houghton Mifflin Harcourt Publishing Company Image Credits: (tr) ©Robert Glusic/Corbis 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. Math Construct arguments and Ones Tenths Hundredths Thousandths Talk MP critique reasoning of others. 2 4 9 5 Explain why it is important to 2 4 9 3 line up the decimal points when comparing decimals. 2=2 4=_ 9=_ 5>_ Since 5 3, then 2.495 2.493, and 2.493 2.495. So, the height of Cloud Peak is ___ the height of Wheeler Peak. Chapter 4 Lesson 4   139  Examples You can use place value to order decimal numbers. 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. STEP 1 STEP 2 Line up the decimal points. There are Underline the hundredths and compare. the same number of ones. Circle the Order from least to greatest. 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 Construct arguments and Talk MP critique reasoning of others. ____ has the greatest height. Explain why you do not compare the digits in the thousandths place to order the heights of the 3 mountains. Try This! Use a place-value chart. What is the order of 1.383, 1.321, 1.456, and 1.32 from greatest to least? W  rite each number in the place-value chart. Compare the digits, beginning with the greatest place value. Ones Tenths Hundredths Thousandths Compare the ones. The ones are the same. 1 3 8 3 Compare the tenths. 4 > 3. 1 1 The greatest number is __. Circle the greatest number in the place-value chart. 1 © Houghton Mifflin Harcourt Publishing Company Compare the remaining hundredths. 8 > 2. The next greatest number is __. Draw a rectangle around the number. Compare the remaining thousandths. 1 > 0. So, the order of the numbers from greatest to least is: _____. 140 Go Math! Grade 5  Name Share and Show Math Board 1. Use the place-value chart to compare the two Ones Tenths Hundredths Thousandths numbers. What is the greatest place-value position where the digits differ? 3 4 7 2 3 4 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 Order from least to greatest. 8. 4.08; 4.3; 4.803; 4.038 9. 1.703; 1.037; 1.37; 1.073 On Your Own Compare. Write , or =. 10. 8.72 8.720 11. 5.4 5.243 12. 1.036 1.306 13. 2.573 2.753 14. 9.300 9.3 15. 6.76 6.759 Order from greatest to least. 16. 2.007; 2.714; 2.09; 2.97 17. 0.275; 0.2; 0.572; 0.725 © Houghton Mifflin Harcourt Publishing Company 18. 5.249; 5.43; 5.340; 5.209 19. 0.678; 1.678; 0.587; 0.687 MP Find the unknown digit to make each statement true. 20. 3.59 > 3.5 1 > 3.572 21. 6.837 > 6.83 > 6.835 22. 2.45 < 2. 6 < 2.461 Chapter 4 Lesson 4   141  Problem Solving · Applications Real World Use the table for problems 23–26. 23. In comparing the height of the mountains, which is the greatest place value where the digits differ? 24. MP How does the height of Mount Steele compare Mountains Over Three Miles High to the height of Mount Blackburn? Compare the Mountain and Location Height (in miles) heights using words. Mount Blackburn, Alaska 3.104 Mount Bona, Alaska 3.134 Mount Steele, Yukon 3.152 25. Explain how to order the heights of the mountains from greatest to least. 26. What if the height of Mount Blackburn were 0.05 mile greater? Would it then be the mountain with the greatest height? Explain. on the Spot © Houghton Mifflin Harcourt Publishing Company Image Credits: (tr) ©L. Clarke/Corbis 27. Orlando kept a record of the total rainfall each month for 5 months. Month Rainfall (in.) March 3.75 April 4.42 May 4.09 June 3.09 July 4.04 Order the months from the least amount of rainfall to the greatest amount of rainfall. Least Greatest 142 Go Math! Grade 5  LESSON 4.4 Name Practice and Homework Compare and Order Decimals Compare. Write , or =. 1. 4.735 < 4.74 2. 2.549 2.549 3. 3.207 3.027 4. 8.25 8.250 5. 5.871 5.781 6. 9.36 9.359 Order from greatest to least. 7. 3.008; 3.825; 3.09; 3.18 8. 0.386; 0.3; 0.683; 0.836 Find the unknown digit to make each statement true. 9. 2.48 > 2.4 1 > 2.463 10. 5.723 < 5.72 < 5.725 11. 7.64 < 7. 5 < 7.68 Problem Solving Real World 12. The completion times for three runners 13. In a discus competition, an athlete threw in a 100-yard dash are 9.75 seconds, the discus 63.37 meters, 62.95 meters, and 9.7 seconds, and 9.675 seconds. Which is 63.7 meters. Order the distances from least the least time? to greatest. © Houghton Mifflin Harcourt Publishing Company 14. Write Math Write a word problem that can be solved by ordering three decimals to thousandths. Include a solution. Chapter 4 Lesson 4   143 Lesson Check Jay, Alana, Evan, and Stacey work together to Student Amount of liquid (liters) complete a science experiment. The table at the Jay 0.8 right shows the amount of liquid left in each of their Alana 1.05 beakers at the end of the experiment. Evan 1.2 Stacey 0.75 15. Whose beaker has the greatest amount of liquid 16. Whose beaker has the least amount of liquid left left in it? in it? Spiral Review 17. Ganyu walked 3.75 miles yesterday. What is the 18. A dance school allows a maximum of word form of 3.75? 15 students per class. If 112 students sign up for dance class, how many classes does the school need to offer to accommodate all the students? 19. Tommy has 3 large jars filled with marbles. He 20. What number is composed of 6 ones, 13 tenths, © Houghton Mifflin Harcourt Publishing Company has a total of 450 marbles. If each jar contains 72 hundredths, and 142 thousandths? the same number of marbles, how many marbles are in each jar? 144  Go Math! Grade 5  CHAPTER 4 Name Lesson 5 Round Decimals I Can use place value to round decimals to a given place. UNLOCK the Problem Real World The Gold Frog of South America is one of the smallest frogs in the world. It is 0.386 of an inch long. What is this Underline the length of the Gold Frog. length rounded to the nearest hundredth of an inch? Is the frog’s length about the same as the length or the width of a large paper clip? One Way Use a place-value chart. Write the number in a place-value chart and circle the digit in the place to which you want to round. In the place-value chart, underline the digit to the right of the place to which you are rounding. If the digit to the right is less than 5, the digit in the place to which you are rounding stays the same. If the digit to the right is 5 or greater, Ones Tenths Hundredths Thousandths the digit in the rounding place increases by 1. 0 3 8 6 Drop the digits after the place to which you are rounding. Think: Does the digit in the rounding place stay the same or increase by 1? So, to the nearest hundredth of an inch, a Gold Frog is about _ inch long. © Houghton Mifflin Harcourt Publishing Company Image Credits: (r) ©Purestock/Alamy Another Way Use place value. The Little Grass Frog is the smallest frog in North America. It is 0.437 inch long. A  What is the length of the frog to the B  What is the length of the frog to the nearest hundredth of an inch? nearest tenth of an inch? 0.437 7>5 0.437 3