Vocabulary rational number terminating decimal repeating decimal

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.

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.

Additional Example 1: Writing Fractions as Decimals Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 1 4 9 5 5 3 A. B. C. 1 .8 1 .6 6 6 0.2 5 1.00 4 5 9.0 3 5.000 – 8 – 3 – 5 20 40 20 – 20 – 40 – 18 20 – 18 1 4 9 5 = 1.8 5 3 = 0.25 20 ≈ 1.67 – 18 2

You can use a calculator to check your division: 1 9 5 Helpful Hint 33 Helpful Hint ÷ 4 = 0.25 1.8 3 1.66…

Check It Out: Example 1 Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 6 5 7 4 5 6 A. B. C. 6.0 5 1.2 –5 10 7.00 5 1 –4 30 .75 –28 20 1.75 5.00 3 –48 20 .8 –18 2 0.83

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

Write each fraction as a decimal. 9 25 A. 0. 3 6 25 9.00 Additional Example 2A: Write Fractions as Terminating and Repeating Decimals Write each fraction as a decimal. 9 25 A. 0. 3 6 ______ ) 25 9.00 –75 The remainder is 0. 150 –150 This is a terminating decimal. 9 25 = 0.36

Write each fraction as a decimal. 17 18 B. 0. 9 4 18 17.00 Additional Example 2B: Write Fractions as Terminating and Repeating Decimals Write each fraction as a decimal. 17 18 B. 0. 9 4 ______ ) 18 17.00 –162 The pattern repeats. 80 – 72 This is a repeating decimal. 8 = 0.94 17 18

Check It Out: Example 2A Write each fraction as a decimal. 11 4 A. 25 11.00 – 8 30 2. 7 5 –28 20 2.75 –20

Check It Out: Example 2B Write each fraction as a decimal. 29 33 A. 33 29.0000 –264 0.8787 0.87 260 –231 290 29

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

Check It Out: Example 3 Write each decimal as a fraction in simplest form. A. 0.065 B. 3.12 0.065 = 65 1,000 = 65 ÷ 5 1,000 ÷ 5 13 200 3.12 = 312 100 = 312 ÷ 4 100 ÷ 4 78 25 or 3 3

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 What the Calculator Shows Completion Rate 1,546 3,875 1546 ÷ ENTER 3875 0.398967742 0.399 His completion rate is 0.399.

Check It Out: Example 4 A basketball player made 11 out of 15 free-throw shots. Find her success rate. Write your answer as a decimal rounded to the nearest thousandth. 11 15 ÷ = 0.73 ≈ 0.733

Write each fraction as a decimal. 1. 3. 4. 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? 16 5 21 8 3.2 2. 2.625 7 10 11 20 0.7 0.55 21 50 69 8 5 8 6. 8.625 or 8 0.70