Objective: You will learn how to convert between fractions and decimals. 1 1

Vocabulary 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.

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

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) 5 3 1 .8 1 .6 6 6 ≈ 1.67 0.2 5 1 4 5 9 3 5 – 8 – 3 – 5 20 4 0 2 0 – 20 – 4 0 – 1 8 2 0 – 1 8 1 4 9 5 = 1.8 = 0.25 2 0 – 1 8 2

Check It Out! Example 2 Write each fraction as a decimal. Round to the nearest hundredth, if necessary. 3 4 6 5 7 3 (A) (B) (C) 2 .3 3 3 1 .2 7 3 0.7 5 ≈ 2.33 3 7 5 6 3 4 – 6 – 2 8 – 5 20 10 10 – 9 – 20 – 10 10 – 9 6 5 3 4 = 1.2 10 = 0.75 – 9 1

Write each fraction as a decimal. Example 3: 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. × = = 0.8 37 50 (B) 37 50 2 2 74 100 Multiply to get a power of ten in the denominator. × = = 0.74

Write each fraction as a decimal. Check It Out! Example 4 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. × = = 0.6 18 25 (B) 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.

Write each decimal as a fraction in simplest form. Example 5: Writing Decimals as Fractions Write each decimal as a fraction in simplest form. (A) 0.018 (B) 1.55 You read the decimal 0.018 as “eighteen thousandths.” Reading Math

Write each decimal as a fraction in simplest form. Example 5: 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 = You read the decimal 0.018 as “eighteen thousandths.” Reading Math

Write each decimal as a fraction in simplest form. Check It Out! Example 6 Write each decimal as a fraction in simplest form. (A) 0.015 (B) 1.30

Write each decimal as a fraction in simplest form. Check It Out! Example 6 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 10 3 200 13 10 = or 1 =

Example 7: 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.

Check It Out! Example 8 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.