Fractions, Decimals, and Percents 6-1 Notes 26 Fractions, Decimals, and Percents 6-1

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?

The model shows that 800 out of 2,000 can be written as , , 200 400 600 800 1,000 1,200 1,400 1,600 1,800 2,000 2 5 4 5 1 5 3 5 5 0.2 0.4 0.6 0.8 1.0 20% 60% 80% 40% 100% 800 2000 2 5 The model shows that 800 out of 2,000 can be written as , , 0.4, or 40%. The students have reached 40% of their goal.

Additional Example 1: Writing Decimals as Percents Write 0.7 as a percent. Method 1: Use pencil and paper. 7 10 70 100 Write the decimal as a fraction with a denominator of 100. 0.7 = = Write the numerator with a percent sign. = 70%

Additional Example 1 Continued Write 0.7 as a percent. Method 2: Use mental math. Move the decimal point two places to the right and add a percent sign. 0.70 = 70% = 70%

Check It Out: Example 1 Write 0.3 as a percent.

Additional Example 2: Writing Fractions as Decimals 5 8 Write as a percent. Method 1: Use pencil and paper. 5 8 = 5 ÷ 8 Use division to write the fraction as a decimal. = .625 = 62.5% Write the decimal as a percent. To divide 5 by 8, use long division and place a decimal point followed by a zero after the 5. 8 5.00 Remember! .625

Check It Out: Example 2 3 5 Write as a percent.

Additional Example 3: Ordering Rational Numbers 4 4 5 Order 17%, 0.25, , 0.1, , and 20% from least to greatest. Step 1: Write the numbers as decimals with the same number of decimal places. 3 4 = 0.75 17% = 0.17 0.25 = 0.25 4 5 = 0.80 0.1 = 0.10 20% = 0.20

Additional Example 3 Continued 4 4 5 Order 17%, 0.25, , 0.1, , and 20% from least to greatest. 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 5

Check It Out: Example 3 1 2 3 4 Order 12%, 0.20, , 0.8, , and 40% from least to greatest.

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 50 27 out of 50 = Think: 27 ÷ 50 divides evenly. Using pencil and paper is the best method. = 0.54 = 54% Write the decimal as a percent. 54% of the people have the newspaper delivered to their home.

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?