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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