1. 2-6 Equivalent Fractions and Decimals Warm Up Write each fraction in the simplest form. 1. 2. 3. 21 63 100 72 1313 1313 4 12 1 7 18 Round each decimal to the nearest HUNDRETH. 4.3.2596. 0.982 5. 42.6817. 112.45823

2. 2-6 Equivalent Fractions and Decimals Problem of the Day Martin recorded how much a bean plant grew each week. The first week the plant grew of an inch, of an inch the second week, and of an inch the third week. During which week did the plant grow the least? week 1 4747 7878 7979

3. 2-6 Equivalent Fractions and Decimals Today’s Goal: Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.

4. 2-6 Equivalent Fractions and Decimals Vocabulary terminating decimal repeating decimal

5. 2-6 Equivalent Fractions and Decimals In baseball, a player’s batting average compares the number of hits with the number of times the player has been at bat. The statistics on the next slide are for the 2006 Major League Baseball season.

6. 2-6 Equivalent Fractions and Decimals Player Hits At Bats Batting Average (thousandths) Miguel Cabrera Ichiro Suzuki Hits at Bats 195 ÷ 576 ≈ 0.339 224 ÷ 695 ≈ 0.322 195 576 195 576 224695 224 695 To convert a fraction to a decimal, divide the numerator by the denominator.

7. 2-6 Equivalent Fractions and Decimals Write each fraction as a decimal. Round to the nearest hundredth, if necessary. Additional Example 1: Writing Fractions as Decimals A. 1414 1.00 9.0 5.000 B. 9595 C. 5353 4 5 3 0.2 – 8 20 – 20 0 1414 = 0.25 5 1 – 5 40.8 – 40 0 9595 = 1.8 1 – 3 20.6 – 18 20 – 18 6 20 – 18 2 5353 ≈ 1.67 6

8. 2-6 Equivalent Fractions and Decimals The decimals 0.75 and 1.2 in Example 1 are terminating decimals because the decimals comes to an end. The decimal 0.333…is a repeating decimal because the decimal repeats a pattern forever. You can also write a repeating decimal with a bar over the repeating part. 0.333… = 0.3 0.8333… = 0.83 0.727272… = 0.72

9. 2-6 Equivalent Fractions and Decimals Write each fraction as a decimal. Additional Example 2: Using Mental Math to Write Fractions as Decimals A. 4545 4545 x 2 = 8 10 = 0.8 Multiply to get a power of ten in the denominator. B. 37 50 x 2 = 74 100 = 0.74 Multiply to get a power of ten in the denominator.

10. 2-6 Equivalent Fractions and Decimals Write each fraction as a decimal. Check It Out: Example 2 A. 3535 3535 x 2 = 6 10 = 0.6 Multiply to get a power of ten in the denominator. B. 18 25 x 4 = 72 100 = 0.72 Multiply to get a power of ten in the denominator.

11. 2-6 Equivalent Fractions and Decimals Write each decimal as a fraction in simplest form. Additional Example 3: Writing Decimals as Fractions A. 0.018 B. 1.55 0.018 = 18 1,000 1.55 = 155 100 = 18 ÷ 2 1,000 ÷ 2 = 155 ÷ 5 100 ÷ 5 = 31 20 or 1 11 20 = 9 500 You read the decimal 0.018 as “eighteen thousandths.” Reading Math

12. 2-6 Equivalent Fractions and Decimals Check It Out: Example 3 Write each decimal as a fraction in simplest form. A. 0.015 B. 1.30 0.015 = 15 1,000 1.30 = 130 100 = 15 ÷ 5 1,000 ÷ 5 = 130 ÷ 10 100 ÷ 10 = 13 10 or 1 3 10 = 3 200

13. 2-6 Equivalent Fractions and Decimals A football player completed 1,546 of the 3,875 passes he attempted. Find his completion rate. Write your answer as a decimal rounded to the nearest thousandth. Additional Example 4: Sports Application Fraction What the Calculator Shows Completion Rate 1,546 3,875 1546 ÷ 3875 ENTER 0.3989677420.399 His completion rate is 0.399.

14. 2-6 Equivalent Fractions and Decimals Check It Out: Example 4 Johnny Unitas, a former professional quarterback, completed 2,830 of the 5,186 passes he attempted. Find his completion rate. Write your answer as a decimal rounded to the nearest thousandth. Fraction What the Calculator Shows Completion Rate 2,830 5,186 2830 ÷ 5186 ENTER 0.54569996 0.546 His completion rate is 0.546.

15. 2-6 Equivalent Fractions and Decimals Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

16. 2-6 Equivalent Fractions and Decimals Lesson Quiz Write each fraction as a decimal. 1. 3. 4. Write each decimal as a fraction in simplest form. 5. 0.42 7. If your soccer team wins 21 out of 30 games, what is your team’s winning rate? 2.625 3.2 21 50 69 8 16 5 2. 21 8 6. 8.625 0.70 7 10 11 20 0.55 0.7 5858 or 8

17. 2-6 Equivalent Fractions and Decimals 1. Which of the following represents the fraction as a decimal? A. 3.4 B. 3.5 C. 3.6 D. 3.7 Lesson Quiz for Student Response Systems 18 5

18. 2-6 Equivalent Fractions and Decimals 2. Which of the following represents the fraction as a decimal? A. 0.65 B. 0.75 C. 0.85 D. 0.95 Lesson Quiz for Student Response Systems 13 20

19. 2-6 Equivalent Fractions and Decimals 3. Which of the following represents the decimal 0.32 as a fraction in simplest form? A. C. B. D. Lesson Quiz for Student Response Systems 8 25 7 25 6 25 1515

20. 2-6 Equivalent Fractions and Decimals 4. Which of the following represents the decimal 6.125 as a fraction in simplest form? A. or 8C. or 6 B. or 6D. or 6 Lesson Quiz for Student Response Systems 49 6 49 8 37 6 31 5 1616 1818 1616 1515

21. 2-6 Equivalent Fractions and Decimals 5. If Rita scores 34 out of 50 in a class test, what is Rita’s scoring rate? A. 0.65 B. 0.66 C. 0.67 D. 0.68 Lesson Quiz for Student Response Systems