Learn to compare and convert between fractions, decimals, and percents.

The word percent means out of 100 The symbol for percent is %. Percents can also be written as fractions or decimals for calculation purposes.

Divide numerator by denominator Decimal  fraction Fraction  decimal Divide numerator by denominator Decimal  fraction Put decimal over place value and simplify Percent  decimal Divide by 100 (moves decimal left 2 places) Decimal  percent Multiply by 100 (moves decimal right 2 places) Fraction  percent Change to decimal then percent (or use a proportion) Percent  fraction Put percent over 100 then simplify

Example A Write 29% as a fraction in simplest form. Write 45% as a fraction in simplest form. 29 45 ÷ 5 9 = 100 100 20 ÷ 5

Example B     9  10 90 2  20 40 = = 90% = = 40% 10 100 5 100  10  20

Example C     5 x 3 x = = 3 100 8 100 = 37.5% = 166.67%

Example D Write the following percents as a decimal. 75% 0.4% 168% = 0.75 = 0.004 = 1.68 Divide by 100 (move decimal 2 places to the left)

Example E Write the following decimals as a percent. 0.62 1 2.3 0.005 = 230% = 0.5% = 62% = 100% Multiply by 100 (move decimal 2 places to the right)

Example F 3 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

Order 17%, 0.25, , 0.1, , and 20% from least to greatest. Example F continued 3 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

Extra Example 1 2 3 4 Order 12%, 0.20, , 0.8, , and 40% from least to greatest. Step 1: Write the numbers as decimals with the same number of decimal places. 1 2 = 0.50 12% = 0.12 0.20 = 0.20 3 4 = 0.75 0.8 = 0.80 40% = 0.40

Extra Example continued 1 2 3 4 Order 12%, 0.20, , 0.8, , and 40% 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. 0.12 < 0.20 < 0.40 < 0.50 < 0.75 < 0.80 From least to greatest, the numbers are: 12%, 0.20, 40%, , , 0.8. 1 2 3 4

Fraction Decimal percent Complete the table below by converting the fraction, decimal, or percent into its other forms. Fraction Decimal percent 1/8 0.625 75% 100% 1.2 5/4

Lesson Quiz 1. Write 0.65 as a percent. 65% 6 10 2. Write as a percent. 60% 3. If 36 out of 80 people surveyed have been on a boat, what percent of these people have been on a boat? 45%

Lesson Quiz for Student Response Systems 1. Which of the following represents 0.52 as a percent? A. 52% B. 26% C. 13% D. 4%

Lesson Quiz for Student Response Systems 2. Which of the following represents 0.08 as a percent? A. 80% B. 40% C. 28% D. 8%

Lesson Quiz for Student Response Systems 7 10 3. Which of the following represents as a percent? A. 7% B. 17% C. 70% D. 77%

Lesson Quiz for Student Response Systems 2 5 4. Order 0.2, 14%, 0.63, and in order from least to greatest. A. 0.2, 14%, , 0.63 C. 14%, 0.2, , 0.63 B. 14%, 0.2, 0.63, D. 0.63, , 0.2, 14% 2 5 2 5 2 5 2 5