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6-1 Fractions, Decimals, and Percents Learn to write decimals and fractions as percents. 6-1 Fractions, Decimals, and Percents The students at Westview Middle School are collecting cans of food for the local food bank. Their goal is to collect 2,000 cans in one month. After 10 days, they have 800 cans of food. What percent of their goal have they reached? 6-1 Fractions, Decimals, and Percents 0 200 1 5 0 0 0 400 0 600 800 2 5 1,000 1,200 1,400 1,600 3 5 4 5 1,800 2,000 5 5 0.2 0.4 0.6 0.8 1.0 20% 40% 60% 80% 100% 800 2 The model shows that 800 out of 2,000 can be written as , , 2000 5 0.4, or 40%. The students have reached 40% of their goal. 6-1 Fractions, Decimals, and Percents Additional Example 1: Writing Decimals as Percents Write 0.7 as a percent. Method 1: Use pencil and paper. 0.7 = 7 70 = 10 100 = 70% Write the decimal as a fraction with a denominator of 100. Write the numerator with a percent sign. 6-1 Fractions, Decimals, and Percents Additional Example 1 Continued Write 0.7 as a percent. Method 2: Use mental math. 0.70 = 70% = 70% Move the decimal point two places to the right and add a percent sign. 6-1 Fractions, Decimals, and Percents Check It Out: Example 1 Write 0.3 as a percent. Method 1: Use pencil and paper. 0.3 = 3 30 = 10 100 = 30% Write the decimal as a fraction with a denominator of 100. Write the numerator with a percent sign. 6-1 Fractions, Decimals, and Percents Check It Out: Example 1 Continued Write 0.93 as a percent. Method 2: Use mental math. 0.30 = 30% = 30% Move the decimal point two places to the right and add a percent sign. 6-1 Fractions, Decimals, and Percents Additional Example 2: Writing Fractions as Decimals Write 5 as a percent. 8 Method 1: Use pencil and paper. 5 =5÷8 8 = .625 = 62.5% Use division to write the fraction as a decimal. Write the decimal as a percent. Remember! To divide 5 by 8, use long division and place a decimal point followed by a zero after the 5. .625 8 5.00 6-1 Fractions, Decimals, and Percents Additional Example 2 Continued Write 5 as a percent. 8 Method 2: Use mental math. 5 8 ● ● 12.5 = 62.5 12.5 100 = 62.5% Write an equivalent fraction with a denominator of 100. Write the numerator with a percent sign. 6-1 Fractions, Decimals, and Percents Check It Out: Example 2 Write 3 as a percent. 5 Method 1: Use pencil and paper. 3 =3÷5 5 = 0.60 = 60% Use division to write the fraction as a decimal. Write the decimal as a percent. 6-1 Fractions, Decimals, and Percents Check It Out: Example 2 Continued Write 3 as a percent. 5 Method 2: Use mental math. 3 5 • • 20 20 = 60 100 Write an equivalent fraction with a denominator of 100. = 60% Write the numerator with a percent sign. 6-1 Fractions, Decimals, and Percents Additional Example 3: Ordering Rational Numbers 4 3 Order 17%, 0.25, , 0.1, 5 , and 20% from 4 least to greatest. Step 1: Write the numbers as decimals with the same number of decimal places. 17% = 0.17 0.25 = 0.25 3 = 0.75 4 0.1 = 0.10 4 = 0.80 5 20% = 0.20 6-1 Fractions, Decimals, and Percents Additional Example 3 Continued 4 Order 17%, 0.25, 3 , 0.1, , and 20% from 5 least to greatest. 4 Step 2: Graph the numbers on the number line. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 Step 3: Compare the decimals. 0.10 < 0.17 < 0.20 < 0.25 < 0.75 < 0.80 From least to greatest, the numbers are: 0.1, 17%, 20%, 0.25, 3 , 4 . 4 5 6-1 Fractions, Decimals, and Percents Check It Out: Example 3 3 1 Order 12%, 0.20, , 0.8, 4 , and 40% from 2 least to greatest. Step 1: Write the numbers as decimals with the same number of decimal places. 12% = 0.20 0.20 = 0.20 1 = 0.50 2 0.8 = 0.80 3 = 0.75 4 40% = 0.40 6-1 Fractions, Decimals, and Percents Check It Out: Example 3 Continued 3 Order 12%, 0.20, 1 , 0.8, , and 40% from 4 least to greatest. 2 Step 2: Graph the numbers on the number line. 0.00 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 1.00 1.10 1.20 Step 3: Compare the decimals. 0.12 < 0.20 < 0.40 < 0.50 < 0.75 < 0.80 From least to greatest, the numbers are: 12%, 0.20, 40%, 1 , 3 , 0.8. 2 4 6-1 Fractions, Decimals, and Percents Additional Example 4: Choosing a Method of Computation Decide whether using pencil and paper, mental math, or a calculator is most useful when solving the following problem. Then solve. If 27 out of 50 people have the newspaper delivered to their home, what percent of these people have the newspaper delivered to their home? 27 Think: 27 ÷ 50 divides evenly. 50 Using pencil and paper is the best method. = 0.54 27 out of 50 = Write the decimal as a percent. = 54% 54% of the people have the newspaper delivered to their home. 6-1 Fractions, Decimals, and Percents Check It Out: Example 4 Decide whether using pencil and paper, mental math, or a calculator is most useful when solving the following problem. Then solve. If 10 out of 50 students have blue backpacks, what percent of the students have blue backpacks? 10 out of 50 = 20 10 = 50 100 Think: The denominator is a multiple of 100. Mental math or pencil and paper is the best method. = 0.20 = 20% Write the decimal as a percent. 20% of the students have blue backpacks. 6-1 Fractions, Decimals, and Percents Lesson Quiz 1. Write 0.65 as a percent. 65% 2. Write 6 as a percent. 10 60% Choose the most useful method of computation. Then solve. 3. If 36 out of 80 people surveyed have been on a boat, what percent of these people have been on a boat? Calculator; 45%