7.NS.2d Convert fractions to decimals using long division. Warm Up Write each fraction in the simplest form. 1. 2. 3. 4. 4 12 1 3 18 46 9 23 21 63 1 3 100 72 25 18 or 1 7 Course 2

Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.

Insert Lesson Title Here Vocabulary terminating decimal ~ a decimal whose digits end. Example: ¾ = 0.75 repeating decimal ~ a decimal which has a pattern in their digits that repeat forever. Example: 1/3 = 0.3

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.

Batting Average (thousandths) Player Hits At Bats Batting Average (thousandths) Lance Berkman Alex Rodriguez Hits at Bats 172 544 172 544 172 ÷ 544 ≈ 0.316 172 601 172 601 172 ÷ 601 ≈ 0.286 To convert a fraction to 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

Insert Lesson Title Here Check It Out: Example 1 Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 3 4 6 5 7 3 A. B. C. 1 .2 2 .3 3 3 0.7 5 3.00 4 5 6.0 3 7.000 – 2 8 – 6 – 5 20 10 10 – 20 – 10 – 9 10 – 9 3 4 6 5 = 1.2 7 3 = 0.75 10 ≈ 2.33 – 9 1

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

Additional Example 2: Using Mental Math to Write Fractions as Decimals Write each fraction as a decimal. 4 5 A. 4 5 2 2 8 10 Multiply to get a power of ten in the denominator. x = = 0.8 37 50 B. 37 50 2 2 74 100 Multiply to get a power of ten in the denominator. x = = 0.74

Write each fraction as a decimal. 3 5 A. Check It Out: Example 2 Write each fraction as a decimal. 3 5 A. 3 5 2 2 6 10 Multiply to get a power of ten in the denominator. x = = 0.6 18 25 B. 18 25 4 4 72 100 Multiply to get a power of ten in the denominator. x = = 0.72

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 = Reading Math You read the decimal 0.018 as “eighteen thousandths.”

Insert Lesson Title Here Check It Out: Example 3 Write each decimal as a fraction in simplest form. A. 0.015 B. 1.30 15 1,000 130 100 0.015 = 1.30 = 15 ÷ 5 1,000 ÷ 5 130 ÷ 10 100 ÷ 10 = = 3 200 3 10 = 13 10 or 1 =

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.

Insert Lesson Title Here 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 ÷ ENTER 5186 0.54569996 0.546 His completion rate is 0.546.

Insert Lesson Title Here 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