Page 1 of 4 Changing Decimals to Fractions BEFORE Now WHY? You wrote decimals and fractions. YouвЂ™ll write a decimal as a fraction. So you can find the miles youвЂ™ve gone on a road trip, as in Ex. 7. You can use models to write decimals as fractions. Word Watch 1 Draw a model for 0.25. Each small square represents one hundredth. The shaded part represents twenty-five hundredths. Review Words simplest form, p. 229 mixed number, p. 244 25 100 0.25 П бЋЏбЋЏ 2 Draw a model for 0.3. Each column represents one tenth. The shaded part represents three tenths. 3 10 0.3 П бЋЏбЋЏ Use a model to write the decimal as a fraction. 1. 0.15 with Solving With practice, you will learn to recognize the fraction form of several common decimals. Here are some examples. 1 2 0.2 П бЋЏбЋЏ 1 4 3 0.75 П бЋЏбЋЏ 4 0.125 П бЋЏбЋЏ 1 8 2 5 0.4 П бЋЏбЋЏ 3. 0.4 4. 0.5 You can use decimal place value to help you write a decimal as a fraction in simplest form. one tenth one hundredth one thousandth 1 0.1 П бЋЏбЋЏ 10 1 0.01 П бЋЏбЋЏ 100 0.001 П бЋЏбЋЏ 1 5 0.5 П бЋЏбЋЏ 0.25 П бЋЏбЋЏ 2. 0.35 EXAMPLE 1 1 1000 Writing Decimals as Fractions Write the decimal as a fraction in simplest form. 8 a. 0.8 П бЋЏ10бЋЏ 4 5 ПбЋЏ 36 бЋЏ b. 0.36 П бЋЏ 100 9 25 П бЋЏбЋЏ Write eight tenths as a fraction. Simplify. Write thirty-six hundredths as a fraction. Simplify. Lesson 5.7 Changing Decimals to Fractions 249 Page 2 of 4 EXAMPLE Science 2 Writing Decimals as Mixed Numbers Planets The length of a planetвЂ™s day is the time it takes the planet to rotate once about its axis. Write each length as a mixed number in simplest form. a. Length of day on Saturn: 10.5 hours b. Length of day on Jupiter: 9.92 hours axis Solution 5 a. 10.5 П 10 бЋЏ10бЋЏ 1 2 П 10 бЋЏбЋЏ Write ten and five tenths as a mixed number. Simplify. 1 2 ANSWER The length of a day on Saturn is 10 бЋЏбЋЏ hours. в– Planets The length of a planetвЂ™s year is the time it takes to revolve once about the Sun. The closer the planet is to the Sun, the shorter its year. The length of JupiterвЂ™s year is 4330.6 Earth days. SaturnвЂ™s year is 10,747 Earth days. Which is closer to the Sun? 92 бЋЏ b. 9.92 П 9 бЋЏ 100 23 25 П 9 бЋЏбЋЏ Write nine and ninety-two hundredths as a mixed number. Simplify. 23 25 ANSWER The length of a day on Jupiter is 9 бЋЏбЋЏ hours. EXAMPLE 3 Decimals with Zeros Write the decimal as a fraction or mixed number in simplest form. 4 бЋЏ a. 2.04 П 2 бЋЏ 100 1 25 П 2 бЋЏбЋЏ 608 бЋЏ b. 0.608 П бЋЏ 1000 76 125 П бЋЏбЋЏ Write two and four hundredths as a mixed number. Simplify. Write six hundred eight thousandths as a fraction. Simplify. Your turn now Write the decimal as a fraction or mixed number in simplest form. 1. 0.4 250 Chapter 5 Number Patterns and Fractions 2. 1.82 3. 2.005 4. 0.405 Page 3 of 4 INTERNET Exercises eWorkbook Plus CLASSZONE.COM More Practice, p. 712 Getting Ready to Practice 1. Vocabulary Explain how you know a fraction is in simplest form. 2. Find the Error Describe 7 100 and correct the error in the solution. 0.7 П бЋЏбЋЏ Copy and complete the statement. ? 3. 0.27 П бЋЏбЋЏ 100 3 4. 2.3 П 2 бЋЏбЋЏ ? ? 5. 6.2 П 6 бЋЏбЋЏ 10 23 6. 5.23 П 5 бЋЏбЋЏ ? 7. Road Trip At your first stop during a road trip, you record the distance youвЂ™ve traveled as 128.4 miles. How could you write this distance as a mixed number in simplest form? Practice and Problem Solving Write the number as a decimal and as a fraction or mixed number. 8. nine tenths 9. fifty-three hundredths 10. two and seven tenths 11. three and eleven hundredths Write the decimal as a fraction or mixed number in simplest form. with Homework Example Exercises 1 8вЂ“9, 12вЂ“13, 24вЂ“26 2 10вЂ“11, 14вЂ“15 3 16вЂ“23 Online Resources CLASSZONE.COM вЂў More Examples вЂў eTutorial plus 12. 0.16 13. 0.72 14. 5.9 15. 9.3 16. 4.06 17. 3.01 18. 0.902 19. 0.806 20. 0.039 21. 0.025 22. 6.036 23. 9.401 In Exercises 24вЂ“26, use the graph. The graph shows the portion of space in a mall occupied by different types of stores. The portions are written as decimals. 24. Which type of store occupies the least space in the mall? the most? 25. Use the circle graph to order the types Mall Space by Store Type Clothing 0.48 Food 0.19 Gifts 0.18 Electronics 0.10 Furniture 0.05 of stores by the portion of space they occupy. 26. Write the decimals from Exercise 25 as fractions in order from least to greatest. Lesson 5.7 Changing Decimals to Fractions 251 Page 4 of 4 27. Honeybee A bee has a length of approximately 0.4708 inch. Write the beeвЂ™s length as a fraction in simplest form. 28. Rainfall The normal monthly precipitation for New Orleans is 4.50 inches in April and 3.05 inches in October. Write the difference of these amounts as a mixed number in simplest form. Challenge Write the decimal as an improper fraction in simplest form. 29. 2.37 30. 6.95 31. 9.86 32. 5.34 Mixed Review Divide. Round your answer to the nearest tenth, if necessary. (Lesson 4.4) 33. 8 П¬ 11 34. 6 П¬ 12 35. 3 П¬ 5 36. 5 П¬ 9 5 1 11 13 37. Order the fractions бЋЏбЋЏ, бЋЏбЋЏ, бЋЏбЋЏ, and бЋЏбЋЏ from least to greatest. (Lesson 5.5) 6 2 36 18 Choose a Strategy Use a strategy from the list to solve the following problem. Explain your choice of strategy. Problem Solving Strategies Guess, Check, and Revise Draw a Diagram в– Perform an Experiment в– Work Backward в– в– 38. You have 2 photographs that are the same size. How many ways can you arrange them (face up and right-side up) next to each other to form a rectangle with twice the area of one photo? Basic Skills Copy and complete the statement. 39. 5 hours П _?_ minutes 40. 367 minutes П _?_ hours _?_ minutes Test-Taking Practice INTERNET State Test Practice CLASSZONE.COM 41. Multiple Choice Which fraction is equivalent to the decimal 0.24? 1 A. бЋЏ24бЋЏ 3 B. бЋЏ25бЋЏ 6 C. бЋЏ25бЋЏ 12 D. бЋЏ25бЋЏ 42. Multiple Choice A survey at a middle school said that 0.65 of the sixth grade students named basketball as their favorite sport. Which fraction represents the decimal 0.65? 3 5 F. бЋЏбЋЏ 252 Chapter 5 Number Patterns and Fractions 13 20 G. бЋЏбЋЏ 7 10 H. бЋЏбЋЏ 3 4 I. бЋЏбЋЏ