4.7 Converting from Decimals to Fractions 4.7 OBJECTIVES 1. Convert a decimal to a common fraction Using what we have learned about place values, you can easily write decimals as common fractions. The following rule is used. Step by Step: To Convert a Terminating Decimal Less Than 1 to a Common Fraction Step 1 Write the digits of the decimal without the decimal point. This will be the numerator of the common fraction. Step 2 The denominator of the fraction is a 1 followed by as many zeros as there are places in the decimal. Example 1 Converting a Decimal to a Common Fraction One place One zero 0.09 Two places 9 100 Two zeros 0.257 7 10 0.7 Three places 257 1000 Three zeros CHECK YOURSELF 1 Write as common fractions. (a) 0.3 (b) 0.311 When a decimal is converted to a common fraction, the common fraction that results should be written in lowest terms. © 2001 McGraw-Hill Companies Example 2 Converting a Decimal to a Common Fraction Convert 0.395 to a fraction and write the result in lowest terms. NOTE Divide the numerator and denominator by 5. 0.395 395 79 1000 200 CHECK YOURSELF 2 Write 0.275 as a common fraction. 379 380 CHAPTER 4 DECIMALS If the decimal has a whole-number portion, write the digits to the right of the decimal point as a proper fraction and then form a mixed number for your result. Example 3 also be written as common fractions, although the process is more complicated. We will limit ourselves to the conversion of terminating decimals in this textbook. Converting a Decimal to a Mixed Number Write 12.277 as a mixed number. 0.277 277 277 , so 12.277 12 1000 1000 CHECK YOURSELF 3 Write 32.433 as a mixed number. Comparing the sizes of common fractions and decimals requires finding the decimal equivalent of the common fraction and then comparing the resulting decimals. Example 4 Comparing the Sizes of Common Fractions and Decimals Which is larger, 3 or 0.38? 8 3 Write the decimal equivalent of . That decimal is 0.375. Now comparing 0.375 and 8 0.38, we see that 0.38 is the larger of the numbers: 0.38 3 8 CHECK YOURSELF 4 Which is larger, 3 or 0.8? 4 CHECK YOURSELF ANSWERS 1. (a) 3 311 ; (b) 10 1000 2. 0.275 11 40 3. 32 433 1000 4. 0.8 3 4 © 2001 McGraw-Hill Companies NOTE Repeating decimals can Name 4.7 Exercises Section Date Write each of the following as a common fraction or mixed number. Write your answer in lowest terms. ANSWERS 1. 0.9 2. 0.3 1. 2. 3. 4. 3. 0.8 4. 0.6 5. 0.37 6. 0.97 5. 6. 7. 0.587 8. 0.3793 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 9. 0.48 10. 0.75 11. 0.58 12. 0.65 13. 0.425 14. 0.116 15. 0.375 16. 0.225 17. 0.136 18. 0.575 19. 20. 19. 0.059 20. 0.067 21. 22. 21. 0.0625 22. 0.0425 23. 24. 23. 6.3 24. 5.7 25. 26. 25. 2.17 26. 3.31 27. © 2001 McGraw-Hill Companies 27. 5.28 28. 15.35 Complete each of the following statements, using the symbol or . 7 29. _____ 0.87 8 5 30. _____ 0.313 16 9 _____ 0.4 31. 25 11 _____ 0.638 32. 17 28. 29. 30. 31. 32. 381 ANSWERS 33. The following table gives the winning percentage for the teams in the American 33. League West. What fraction of their games has each team won? 34. Team Winning Percentage Texas Oakland Seattle Anaheim 0.595 0.552 0.494 0.415 34. The following table gives the winning percentages of the top five coaches in NFL history. What fraction of his games has each coach won? Coach Percentage Don Shula George Halas Tom Landry Curly Lambeau Chuck Knoll 0.676 0.672 0.606 0.624 0.566 9 10 3 15. 8 1. 27. 5 382 4 5 3. 17. 7 25 5. 17 125 29. 37 100 19. 7. 59 1000 31. 587 1000 9. 12 25 11. 29 50 1 3 23. 6 16 10 119 69 247 83 , , , 33. 200 125 500 200 21. 13. 25. 2 17 100 17 40 © 2001 McGraw-Hill Companies Answers Using Your Calculator to Convert Between Decimals and Fractions A calculator is very useful in converting common fractions to decimals. Just divide the numerator by the denominator, and the decimal equivalent will be in the display. Example 1 Converting Fractions to Decimals Find the decimal equivalent of 7 . 16 7 16 Display 0.4375 0.4375 is the decimal equivalent of 7 . 16 CHECK YOURSELF 1 Find the decimal equivalent of 5 . 16 Often, you will want to round the result in the display. Example 2 Converting Fractions to Decimals NOTE Some calculators show Find the decimal equivalent of the 0 to the left of the decimal point and seven digits to the right. Others omit the 0 and show eight digits to the right. Check yours with this example. 5 24 Display 0.2083333 5 0.21 24 © 2001 McGraw-Hill Companies 5 to the nearest hundredth. 24 (nearest hundredth) CHECK YOURSELF 2 Find the decimal equivalent of 7 to the nearest hundredth. 29 To find the decimal equivalent of a mixed number, use the following sequence. 383 384 CHAPTER 4 DECIMALS Example 3 NOTE There are several ways to do this, depending on the calculator you are using. For example, Converting Mixed Numbers to Decimals 5 Change 7 to a decimal. 8 7 5 8 5 8 7 Display 7.625 CHECK YOURSELF 3 3 Find the decimal equivalent of 3 . 8 Depending on the calculator you are using, the result may be rounded at its last displayed digit. Example 4 Converting Fractions to Decimals 5 For : 9 5 9 Display 0.555555555 or 0.5555555556 Rounded display CHECK YOURSELF 4 Find the decimal equivalent of 7 . 11 CHECK YOURSELF ANSWERS 1. 0.3125 2. 0.24 3. 3.375 4. 0.63636363 or 0.63636364 © 2001 McGraw-Hill Companies will work on most scientific calculators. Try it on yours. Name Calculator Exercises Section Date Find the decimal equivalents. 1. 7 8 2. 11 16 ANSWERS 1. 2. 3. 9 16 4. 7 hundredth 24 3. 4. 5. 5. 5 thousandth 32 6. 11 thousandth 75 6. 7. 8. 7. 3 use bar notation 11 8. 7 use bar notation 11 9. 10. 11. 16 9. use bar notation 33 4 10. 3 5 12. 13. 14. 11. 3 7 8 12. 8 3 16 15. 16. 17. © 2001 McGraw-Hill Companies Convert each decimal to a fraction. 13. 0.3 14. 0.55 15. 0.305 16. 0.1 17. 0.875 18. 0.125 18. 385 Answers 1. 0.875 3. 0.5625 61 15. 200 5. 0.156 7. 0.27 9. 0.48 11. 3.875 7 17. 8 © 2001 McGraw-Hill Companies 3 13. 10 386