1. 2-10 Equivalent Fractions and Decimals Course 2 Warm Up Warm Up Problem of the Day Problem of the Day Lesson Presentation Lesson Presentation

2. Warm Up Write each fraction in the simplest form. 1. 2. 3. 4. Course 2 2-10 Equivalent Fractions and Decimals 18 46 21 63 100 72 1313 1313 4 12 9 23 25 18 or 1 7 18

3. 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 Course 2 2-10 Equivalent Fractions and Decimals 4747 7878 7979

4. Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating. Course 2 2-10 Equivalent Fractions and Decimals

5. Vocabulary terminating decimal repeating decimal Insert Lesson Title Here Course 2 2-10 Equivalent Fractions and Decimals

6. Course 2 2-10 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 2004 Major League Baseball season.

7. Course 2 2-10 Equivalent Fractions and Decimals Player Hits At Bats Batting Average (thousandths) Lance Berkman Alex Rodriguez Hits at Bats 172 ÷ 544 ≈ 0.316 172 ÷ 601 ≈ 0.286 172 544 172 544 172601 172 601 To convert a fraction to a decimal, divide the numerator by the denominator.

8. Write each fraction as a decimal. Round to the nearest hundredth, if necessary. Additional Example 1: Writing Fractions as Decimals Course 2 2-10 Equivalent Fractions and 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

9. Course 2 2-10 Equivalent Fractions and Decimals You can use a calculator to check your division: 1 9 5 33 Helpful Hint ÷ 4 = 0.25 ÷ 5 = 1.8 ÷ 3 = 1.66…

10. Check It Out: Example 1 Insert Lesson Title Here Course 2 2-10 Equivalent Fractions and Decimals Write each fraction as a decimal. Round to the nearest hundredth, if necessary. A. 3434 3.00 6.0 7.000 B. 6565 C. 7373 4 5 3 0.7 – 2 8 20 – 20 0 3434 = 0.75 5 1 – 5 10.2 – 10 0 6565 = 1.2 2 – 6 10.3 – 9 10 – 9 3 10 – 9 1 7373 ≈ 2.33 3

11. Course 2 2-10 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

12. Write each fraction as a decimal. Additional Example 2: Using Mental Math to Write Fractions as Decimals Course 2 2-10 Equivalent Fractions and 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.

13. Write each fraction as a decimal. Check It Out: Example 2 Course 2 2-10 Equivalent Fractions and Decimals 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.

14. Write each decimal as a fraction in simplest form. Additional Example 3: Writing Decimals as Fractions Course 2 2-10 Equivalent Fractions and Decimals 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

15. Check It Out: Example 3 Insert Lesson Title Here Course 2 2-10 Equivalent Fractions and Decimals 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

16. 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 Course 2 2-10 Equivalent Fractions and Decimals Fraction What the Calculator Shows Completion Rate 1,546 3,875 1546 ÷ 3875 ENTER 0.3989677420.399 His completion rate is 0.399.

17. Check It Out: Example 4 Insert Lesson Title Here Course 2 2-10 Equivalent Fractions and Decimals 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.

18. 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 Insert Lesson Title Here 21 50 69 8 Course 2 2-10 Equivalent Fractions and Decimals 16 5 2. 21 8 6. 8.625 0.70 7 10 11 20 0.55 0.7 5858 or 8