2 11 Equivalent Fractions and Decimals Vocabulary rational

2 -11 Equivalent Fractions and Decimals Vocabulary rational number terminating decimal repeating decimal

2 -11 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 below are for the 2006 Major League Baseball season.

2 -11 Equivalent Fractions and Decimals A rational number is a number that can be written as a fraction with an integer for its numerator and a nonzero integer for its denominator. To write a rational number as a decimal, divide the numerator by the denominator.

2 -11 Equivalent Fractions and Decimals Additional Example 1: Writing Fractions as Decimals Write each fraction as a decimal. Round to the nearest hundredth, if necessary. A. 1 4 0. 2 5 4 1. 00 – 8 20 – 20 0 1 = 0. 25 4 B. 9 5 1. 8 5 9. 0 – 5 40 – 40 0 9 = 1. 8 5 C. 5 3 1. 6 6 6 3 5. 000 – 3 20 – 18 5 20 3 ≈ 1. 67 – 18 2

2 -11 Equivalent Fractions and Decimals Helpful Hint You can use a calculator to check your division: 1 ÷ 4 9 ÷ 5 = 1. 8 5 ÷ 3 = 1. 66… 33 = 0. 25

2 -11 Equivalent Fractions and Decimals Check It Out: Example 1 Write each fraction as a decimal. Round to the nearest hundredth, if necessary. B. 7 4 A. 6 5 1. 2 5 6. 0 – 5 10 1. 2 1. 75 5 7. 00 – 4 30 – 28 20 C. 5 6 1. 75 0. 8 3 3 5. 00 – 48 20 – 18 2 0. 83

2 -11 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

2 -11 Equivalent Fractions and Decimals Additional Example 2 A: Write Fractions as Terminating and Repeating Decimals Write each fraction as a decimal. 9 A. 25 0. 3 6 ______ 25 ) 9. 00 – 75 150 – 150 0 9 = 0. 36 25 The remainder is 0. This is a terminating decimal.

2 -11 Equivalent Fractions and Decimals Additional Example 2 B: Write Fractions as Terminating and Repeating Decimals Write each fraction as a decimal. 17 B. 18 0. 9 4 ______ 18 )17. 00 – 162 80 – 72 8 17 = 0. 94 18 The pattern repeats. This is a repeating decimal.

2 -11 Equivalent Fractions and Decimals Check It Out: Example 2 A Write each fraction as a decimal. A. 11 4 2. 75 25 11. 00 – 8 30 – 28 20 – 20 0 2. 75

2 -11 Equivalent Fractions and Decimals Check It Out: Example 2 B Write each fraction as a decimal. 29 A. 33 0. 8787 33 29. 0000 – 264 260 – 231 29 0. 87

2 -11 Equivalent Fractions and Decimals Additional Example 3: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. A. 0. 018 18 1, 000 18 ÷ 2 = 1, 000 ÷ 2 9 = 500 0. 018 = B. 1. 55 = 100 = 155 ÷ 5 100 ÷ 5 31 or 1 11 = 20 20 Reading Math You read the decimal 0. 018 as “eighteen thousandths. ”

2 -11 Equivalent Fractions and Decimals Check It Out: Example 3 Write each decimal as a fraction in simplest form. A. 0. 065 = 65 1, 000 = 65 ÷ 5 1, 000 ÷ 5 = 13 200 B. 3. 12 = 100 = 312 ÷ 4 100 ÷ 4 = 78 25 78 or 3 3 25 25

2 -11 Equivalent Fractions and Decimals Additional Example 4: Sports Application 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. Fraction 1, 546 3, 875 What the Calculator Shows 1546 ÷ 3875 ENTER 0. 398967742 His completion rate is 0. 399. Completion Rate 0. 399

2 -11 Equivalent Fractions and Decimals Check It Out: Example 4 A basketball player made 11 out of 15 freethrow shots. Find her success rate. Write your answer as a decimal rounded to the nearest thousandth. 11 15 11 ÷ 15 = 0. 73 ≈ 0. 733

2 -11 Equivalent Fractions and Decimals Lesson Quiz Write each fraction as a decimal. 1. 3. 16 5 7 10 3. 2 2. 0. 7 4. 21 8 11 20 2. 625 0. 55 Write each decimal as a fraction in simplest form. 69 or 8 5 21 6. 8. 625 5. 0. 42 8 50 8 7. If your soccer team wins 21 out of 30 games, what is your team’s winning rate? 0. 70