Learn to compare and order decimals, fractions, and percents.

Percents are ratios that compare a number to 100.

Think of the % symbol as meaning per 100 or /100. 75% = 75/100 = 0.75 Reading Math

To convert a fraction to a decimal, divide the numerator by the denominator. 1 8 = 1 ÷ 8 = 0.125 To convert a decimal to a percent, multiply by 100 and insert the percent symbol. 0.125  100  12.5%

Example 1: Finding Equivalent Ratios and Percents Find the missing ratio or percent equivalent for each letter a–g on the number line. 10 100 = 1 10 a: 10% =

Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 4 = b: 0.25 = 25%

Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 40 100 = 4 10 = 2 5 c: 40% =

Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 3 5 = d: 0.60 = 60%

Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 2 3 % = 66 2 3 e: 0.666 =

Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 1 2 % = 87 875 1000 = 7 8 f: 0.875 =

Example 1 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. 125 100 = 5 4 = 1 4 g: 125% =

Example 2 Find the missing ratio or percent equivalent for each letter a–g on the number line. c a b e d 50% 12 % f g 3 8 25% 1 2 5 75% 1 2 % = 12 125 1000 = 1 8 a: 0.125 =

Example 2 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. c a b e d 50% 12 % f g 3 8 25% 1 2 5 75% 25 100 = 1 4 b: 25% =

Example 2 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. c a b e d 50% 12 % f g 3 8 25% 1 2 5 75% 1 2 3 8 = c: 0.375 = 37 %

Example 2 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. c a b e d 50% 12 % f g 3 8 25% 1 2 5 75% 50 100 = 1 2 d: 50% =

Example 2 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. c a b e d 50% 12 % f g 3 8 25% 1 2 5 75% 1 2 5 8 = e: 0.625 = 62 %

Example 2 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. c a b e d 50% 12 % f g 3 8 25% 1 2 5 75% 75 100 = 3 4 f: 75% =

Example 2 Continued Find the missing ratio or percent equivalent for each letter a–g on the number line. c a b e d 50% 12 % f g 3 8 25% 1 2 5 75% 100 = 100% g: 1 =

Example 3: Comparing Fractions, Decimals, and Percents Compare. Write <, >, or =. 40% 1 4 1 4 = 0.25 Write as a decimal. 0.25 < 0.40 Compare. 1 4 < 40% When multiplying a decimal by 100, simply move the decimal point two spaces to the right. Remember!

Example 4: Comparing Fractions, Decimals, and Percents Compare. Write <, >, or =. 0.893 50% 50% = 0.50 Write as a decimal. 0.893 > 0.50 Compare. 0.893 > 50%

Example 5 Compare. Write <, >, or =. 65% 3 4 3 4 = 0.75 Write as a decimal. 0.75 > 0.65 Compare. 3 4 > 65%

Example 6 Compare. Write <, >, or =. 0.136 20% 20% = 0.20 Write as a decimal. 0.136 < 0.20 Compare. 0.136 < 20%

Example 7: Ordering Fractions, Decimals, and Percents 3 4 Write 0.075%, , 0.41, and 100% in order from least to greatest. 3 4 = 0.75 Write as decimals. 100% = 1.00 0.075% = 0.00075 0.075% < 41% < 75% < 100% Compare. 3 4 0.075%, 0.41, , 100%

Example 8 1 2 Write 35%, 0.25, , and 200% in order from least to greatest. 1 2 = 0.50 Write as decimals. 35% = 0.35 200% = 2.00 25% < 35% < 50% < 200% Compare. 1 2 0.25, 35%, , 200%

Lesson Quiz for Student Response Systems Lesson Quizzes Standard Lesson Quiz Lesson Quiz for Student Response Systems 25

Lesson Quiz: Part I Find each equivalent value. 1. as a percent 2. 20% as a fraction 3. as a decimal Compare. Write <, >, or =. 4. 30% 5. 0.650 97% 3 8 37.5% 1 5 5 8 0.625 7 11 > <

Lesson Quiz: Part II 6. Write 245%, , 0.133, and 66.6% in order from least to greatest. 5. About 342,000 km2 of Greenland’s total area (2,175,000 km2) is not covered with ice. To the nearest percent, what percent of Greenland’s total area is not covered with ice? 1 5 1 5 0.133, , 66.6%, 245% 16%

Lesson Quiz for Student Response Systems 5 9 1. Identify the equivalent value of as a percent. A. 45.3% B. 55.5% C. 78.3% D. 86.5% 28

Lesson Quiz for Student Response Systems 2. Identify the equivalent value of 45% as a fraction. A. B. C. D. 29

Lesson Quiz for Student Response Systems 3 8 3. Identify the equivalent value of as a decimal. A. 0.252 B. 0.375 C. 0.456 D. 0.698 30

Lesson Quiz for Student Response Systems 4. Identify the correct symbol to compare. 0.430___50% A. > B. < C. = D. > 31