3 9 Equivalent Fractions and Decimals Warm Up

3 -9 Equivalent Fractions and Decimals Warm Up Problem of the Day Lesson Presentation Course 2

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

3 -9 Equivalent Fractions and Decimals Problem of the Day For Martin’s 4 -H project he recorded how much a bean plant grew each week. The first week the plant grew 47 of an inch. It grew 78 of an inch the second week and 79 of an inch the third week. During which week did the plant grow the least? week 1 Course 2

3 -9 Equivalent Fractions and Decimals Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating. Course 2

Fractions Decimals 3 -9 Equivalent Insert Lesson Titleand Here Vocabulary terminating decimal repeating decimal Course 2

3 -9 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 2001 Major League Baseball season. Course 2

3 -9 Equivalent Fractions and Decimals Hits At Bats Mark Grace 142 476 Cal Ripken, Jr. 114 477 142 476 114 477 Ivan Rodriguez 136 442 136 ÷ 442 ≈ 0. 308 Sammy Sosa 577 289 ÷ 577 ≈ 0. 328 Player 189 Hits at Bats Batting Average (thousandths) 142 ÷ 476 ≈ 0. 298 114 ÷ 477 ≈ 0. 239 To convert a fraction to a decimal, divide the numerator by the denominator. Course 2

3 -9 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 Course 2 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

3 -9 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 Course 2 = 0. 25

Fractions Decimals 3 -9 Equivalent Insert Lesson Titleand Here Try This: Example 1 Write each fraction as a decimal. Round to the nearest hundredth, if necessary. A. 3 4 0. 7 5 4 3. 00 – 28 20 – 20 0 3 = 0. 75 4 Course 2 B. 6 5 1. 2 5 6. 0 – 5 10 – 10 0 6 = 1. 2 5 C. 7 3 2. 3 3 7. 000 – 6 10 – 9 7 10 3 ≈ 2. 33 – 9 1

3 -9 Equivalent Fractions and Decimals The decimals 0. 75 and 1. 2 in Example 1 are terminating decimals because the decimal 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 Course 2 0. 8333… = 0. 83 0. 727272… = 0. 72

3 -9 Equivalent Fractions and Decimals You can use place value to convert a terminating decimal to a fraction. Place Thousands Place Value 1, 000 Course 2 Hundreds Tens Ones 100 10 1 · Tenths Hundredths Thousandths 0. 1 = 1 10 0. 01 = 1 100 0. 001 = 1 1, 000

3 -9 Equivalent Fractions and Decimals Additional Example 2: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. B. – 0. 6 A. 0. 018 = 18 1, 000 = 18 ÷ 2 1, 000 ÷ 2 = 9 500 Course 2 C. 1. 55 – 0. 6 = – 6 10 = – 6÷ 2 = 3 5 10 ÷ 2 – 1. 55 155 = 100 = 155 ÷ 5 100 ÷ 5 31 or 1 11 = 20 20

Fractions Decimals 3 -9 Equivalent Insert Lesson Titleand Here Try This: Example 2 Write each decimal as a fraction in simplest form. B. – 0. 8 A. 0. 015 = 15 1, 000 = 15 ÷ 5 1, 000 ÷ 5 = 3 200 Course 2 C. 1. 30 – 0. 8 = – 8 10 = – 8÷ 2 = 4 5 10 ÷ 2 – 1. 30 130 = 100 = 130 ÷ 10 100 ÷ 10 13 or 1 3 = 10 10

3 -9 Equivalent Fractions and Decimals Additional Example 3: 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. 398967749 His completion rate is 0. 399. Course 2 Completion Rate 0. 399

Fractions Decimals 3 -9 Equivalent Insert Lesson Titleand Here Try This: Example 3 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 2, 830 5, 186 What the Calculator Shows 2830 ÷ 5186 ENTER 0. 54569996 His completion rate is 0. 546. Course 2 Completion Rate 0. 546

Fractions Decimals 3 -9 Equivalent Insert Lesson Titleand Here Lesson Quiz Write each fraction as a decimal. 1. 16 5 3. 2 2. 21 8 2. 625 Write each decimal as a fraction in simplest form. 21 4. 8. 625 69 50 8 5. If your soccer team wins 21 out of 30 games, what is your team’s winning rate? 3. 0. 42 0. 70 Course 2