2 10 Equivalent Fractions and Decimals Warm Up

2 -10 Equivalent Fractions and Decimals Warm Up Problem of the Day Lesson Presentation Lesson Quizzes Objective: Students write fractions as decimals, and vice versa, and determine whether a decimal is terminating or repeating

2 -10 Equivalent Fractions and Decimals Warm Up Write each fraction in the simplest form. 1. 3. 4 12 21 63 18 46 1 3 2. 1 3 4. 100 72 9 23 25 or 1 7 18 18

2 -10 Equivalent Fractions and Decimals Problem of the Day Martin recorded how much a bean plant grew each week. The first week the plant grew 47 of an inch, 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

2 -10 Equivalent Fractions and Decimals Learn to write fractions as decimals, and vice versa, and to determine whether a decimal is terminating or repeating.

2 -10 Equivalent Fractions and Decimals Vocabulary terminating decimal repeating decimal

2 -10 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 2006 Major League Baseball season.

2 -10 Equivalent Fractions and Decimals Player Hits At Hits Bats at Bats Miguel Cabrera 195 576 Ichiro Suzuki 224 695 195 576 224 695 Batting Average (thousandths) 195 ÷ 576 ≈ 0. 339 224 ÷ 695 ≈ 0. 322 To convert a fraction to a decimal, divide the numerator by the denominator.

2 -10 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 -10 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 -10 Equivalent Fractions and Decimals Check It Out: 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 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

2 -10 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 -10 Equivalent Fractions and Decimals Additional Example 2: Using Mental Math to Write Fractions as Decimals Write each fraction as a decimal. 4 A. 5 4 x 2 = 8 5 2 10 37 B. 50 Multiply to get a power of ten in the denominator. = 0. 8 37 x 2 = 74 50 2 100 = 0. 74 Multiply to get a power of ten in the denominator.

2 -10 Equivalent Fractions and Decimals Check It Out: Example 2 Write each fraction as a decimal. 3 A. 5 3 x 2 = 6 5 2 10 18 B. 25 Multiply to get a power of ten in the denominator. = 0. 6 18 x 4 = 72 25 4 100 = 0. 72 Multiply to get a power of ten in the denominator.

2 -10 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 -10 Equivalent Fractions and Decimals Check It Out: Example 3 Write each decimal as a fraction in simplest form. A. 0. 015 = 15 1, 000 B. 1. 30 = 100 = 15 ÷ 5 1, 000 ÷ 5 = 130 ÷ 10 100 ÷ 10 = 3 200 3 13 or 1 = 10 10

2 -10 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 -10 Equivalent Fractions and Decimals 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 2, 830 5, 186 What the Calculator Shows 2830 ÷ 5186 ENTER 0. 54569996 His completion rate is 0. 546. Completion Rate 0. 546

2 -10 Equivalent Fractions and Decimals Lesson Quizzes Standard Lesson Quiz for Student Response Systems

2 -10 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

2 -10 Equivalent Fractions and Decimals Lesson Quiz for Student Response Systems 1. Which of the following represents the fraction 18 as a decimal? 5 A. 3. 4 B. 3. 5 C. 3. 6 D. 3. 7

2 -10 Equivalent Fractions and Decimals Lesson Quiz for Student Response Systems 2. Which of the following represents the fraction 13 as a decimal? 20 A. 0. 65 B. 0. 75 C. 0. 85 D. 0. 95

2 -10 Equivalent Fractions and Decimals Lesson Quiz for Student Response Systems 3. Which of the following represents the decimal 0. 32 as a fraction in simplest form? A. C. 8 25 6 25 B. D. 7 25 1 5

2 -10 Equivalent Fractions and Decimals Lesson Quiz for Student Response Systems 4. Which of the following represents the decimal 6. 125 as a fraction in simplest form? 1 A. 49 or 8 C. 37 or 6 1 6 6 B. 49 or 6 8 1 8 D. 31 or 6 1 5 5

2 -10 Equivalent Fractions and Decimals Lesson Quiz for Student Response Systems 5. If Rita scores 34 out of 50 in a class test, what is Rita’s scoring rate? A. 0. 65 B. 0. 66 C. 0. 67 D. 0. 68