Preparation for NS1.1 Compare and order positive and negative fractions, decimals, and mixed numbers and place them on a number line. Also covered: NS2.4 California Standards

VOCABULARY CARDS Fraction to Decimal Decimal to Fraction Terminating Decimal Repeating Decimal

Batting Average (thousandths) In baseball, a player’s batting average compares the number of hits with the number of times the player has been at bat. 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.

Teacher 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 1A. 1B. 1C. 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 5 3 = 1.8 = 0.25 20 ≈ 1.67 – 18 2

Student Practice 1: Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 3 4 6 5 7 3 1A. 1B. 1C. 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 7 3 = 1.2 = 0.75 10 ≈ 2.33 – 9 1

The decimals 0.75 and 1.2 are terminating decimals because the decimals comes to an end. The decimal 0.333… is a repeating decimal because it includes a group of one or more digits (where all digits are not zero) that repeats 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

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

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

You can also use place value to write a terminating decimal as a fraction. Use the place value of the last digit to the right of the decimal point as the denominator of the fraction.

Teacher Example 3: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. 3A. 0.018 3B. 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

Student Practice 3: Write each decimal as a fraction in simplest form. 3A. 0.015 3B. 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 =

Teacher 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. 0.3989… Divide the numerator by the denominator. His completion rate is 0.399.

Student Practice 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. 0.5456… Divide the numerator by the denominator. His completion rate is 0.546.

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