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

3-9 Equivalent Fractions and Decimals Warm Up Course 2 3-9 Equivalent Fractions and Decimals 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

3-9 Equivalent Fractions and Decimals Problem of the Day 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 of an inch. It grew of an inch the second week and of an inch the third week. During which week did the plant grow the least? 4 7 7 8 7 9 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.

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

3-9 Equivalent Fractions and Decimals 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.

Batting Average (thousandths) Course 2 3-9 Equivalent Fractions and Decimals Player Hits At Bats Batting Average (thousandths) Mark Grace Cal Ripken, Jr. Ivan Rodriguez Sammy Sosa Hits at Bats 142 476 142 476 142 ÷ 476 ≈ 0.298 114 477 114 477 114 ÷ 477 ≈ 0.239 136 442 136 442 136 ÷ 442 ≈ 0.308 289 577 189 577 289 ÷ 577 ≈ 0.328 To convert a fraction to a decimal, divide the numerator by the denominator.

Additional Example 1: Writing Fractions as Decimals 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. 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

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

Insert Lesson Title Here Course 2 3-9 Equivalent Fractions and Decimals Insert Lesson Title Here Try This: 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

3-9 Equivalent Fractions and Decimals Course 2 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 0.8333… = 0.83 0.727272… = 0.72

3-9 Equivalent Fractions and Decimals Course 2 3-9 Equivalent Fractions and Decimals You can use place value to convert a terminating decimal to a fraction. Place Thousands Hundreds Tens Ones · Tenths Hundredths Thousandths Place Value 1,000 100 10 1 0.1 = 0.01 = 0.001 =

Additional Example 2: Writing Decimals as Fractions Course 2 3-9 Equivalent Fractions and Decimals Additional Example 2: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. A. 0.018 B. –0.6 C. 1.55 18 1,000 6 10 0.018 = 155 100 –0.6 = – 1.55 = 18 ÷ 2 1,000 ÷ 2 6 ÷ 2 10 ÷ 2 155 ÷ 5 100 ÷ 5 = = – = 11 20 3 5 31 20 9 500 = – or 1 = =

Insert Lesson Title Here Course 2 3-9 Equivalent Fractions and Decimals Insert Lesson Title Here Try This: Example 2 Write each decimal as a fraction in simplest form. A. 0.015 B. –0.8 C. 1.30 15 1,000 8 10 0.015 = 130 100 –0.8 = – 1.30 = 15 ÷ 5 1,000 ÷ 5 8 ÷ 2 10 ÷ 2 130 ÷ 10 100 ÷ 10 = = – = 3 10 4 5 13 10 3 200 = – or 1 = =

Additional Example 3: Sports Application Course 2 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 What the Calculator Shows Completion Rate 1,546 3,875 1546 ÷ ENTER 3875 0.398967749 0.399 His completion rate is 0.399.

Insert Lesson Title Here Course 2 3-9 Equivalent Fractions and Decimals Insert Lesson Title 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 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 Course 2 3-9 Equivalent Fractions and Decimals Insert Lesson Title Here Lesson Quiz Write each fraction as a decimal. 1. Write each decimal as a fraction in simplest form. 3. 0.42 5. 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 21 50 69 8 4. 8.625 0.70