6-3 Percents Greater Than 100% Or Less Than 1% 6-3 1

6-3 Percents Greater Than 100% or Less Than 1% 6-3 1. Plan

What You’ll Learn Check Skills You’ll Need For help, go to Lesson 6-1. Lesson Preview OBJECTIVE To use percents PowerPoint 1 Model each percent. 1–3. See below left. greater than 100% or less than 1% 1. 40% 2. 1% 3. 100% Check Skills You’ll Need Writing and Modeling Percents ...And Why Write each ratio as a percent. Lesson 6-1: Examples 2, 4. Extra To ﬁnd a percent in the Practice p. 689. 1 1% 49 98% 19 2 8% U.S. House, as in Example 4 4.100 5.50 6.20 95% 7. 25 Lesson Resources OBJECTIVE Interactive lesson includes instant self-check, tutorials, and activities. 1 Using Percents Greater Than 100% or Less Than 1% Teaching Resources Practice, Reteaching, Enrichment

1. A percent is a ratio that compares a number to 100. If the number Reaching All Students compared to 100 is greater than 100, the percent is greater than 100%. If Practice Workbook 6-3 the number compared to 100 is less than 1, the percent is less than 1%. Spanish Practice Workbook 6-3 Guided Problem Solving 6-3 Real Technology Activities 25 1 EXAMPLE Rewriting Percents Greater Than 100 World Nutrition You get 110% of the Recommended Daily Allowance of vitamin Presentation Assistant Plus! 2. C from one half of a grapefruit. Write 110% as a decimal and as a fraction. Transparencies • Check Skills You’ll Need 6-3 110% = 1.10 d To write as a decimal, move the decimal point two places to the left. • Problem of the Day 6-3 110 • Additional Examples 6-3 110% = d To write as a fraction, use the deﬁnition of percent. 100 • Student Edition Answers 6-3 11 1 = d • Lesson Quiz 6-3 10,or110 Simplify the fraction. 1 • Classroom Aid 9–11 110% equals 1.10 in decimal form and1 10 in fraction form. PH Presentation Pro CD-ROM 6-3 5 1 Check Understanding 1 Write 125% as a decimal and as a fraction in simplest form. 1.25; 4 or 14

Computer Test Generator CD 2 EXAMPLE Rewriting Percents Less Than 1 Technology 3. Write 0.7% as a decimal and a fraction. Resource Pro® CD-ROM 0.7% = 0.007 d To write as a decimal, move the decimal point two places to the left. Computer Test Generator CD = 0.7 d PH Presentation Pro CD-ROM 0.7% 100 To write as a fraction, use the deﬁnition of percent. = 0.7 ? 10 d www.PHSchool.com ? Multiply numerator and denominator by 10. 100 10 Student Site = 7 d • Teacher Web Code: abk-5500 1,000 Simplify as a fraction with a whole number numerator. • Self-grading Lesson Quiz 7 0.7% equals 0.007 in decimal form and1,000 in fraction form. PH SuccessNet Teacher Center • Lesson Planner Check Understanding 2 Write 0.35% as a decimal and as a fraction in simplest form. 0.0035; 7 2,000 • Resources

6-3 Percents Greater Than 100% or Less Than 1% 301 Plus

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S Ongoing Assessment and Intervention Before the Lesson During the Lesson After the Lesson Diagnose prerequisite skills using: Monitor progress using: Assess knowledge using: • Check Skills You’ll Need • Check Understanding • Lesson Quiz • Additional Examples • Computer Test Generator CD • Test Prep 301 2. Teach A mixed number represents a percent greater than 100%. Real 3 EXAMPLE Writing Mixed Numbers as Percents World Math Background Entertainment You want to see a movie. The cost of admission to a movie is A percent can be greater than 7 1 8 times the cost of renting a video. Write this mixed number as a percent. 100% or less than 1%. Percents greater than 100% convert to 7 = 1.875 d 1 8 178 Use a calculator. mixed numbers. Percents less 1% 1 ==1.87.5 187.5% d Move the decimal point two places to the right. convert to fractions less than 100 . u 150 u 1 The cost of admission to a movie is 187.5% of the cost of renting a video. 150% 100 12 0.15% u 15 u 3 10,000 2,000 Check Understanding 3 Write each mixed number or decimal as a percent. When necessary, round To convert a mixed number to a to the nearest hundredth of a percent. percent, ﬁrst write it as a decimal. 5 4 341.67% 280% 171% 400.5% a.312 b.25 c. 1.71 d. 4.005 Teaching Notes A proper fraction represents a percent less than 100%. 1 EXAMPLE Visual Learners Provide students with two 10 x 10 4 EXAMPLE Real-World Problem Solving grids to model percents greater than 100. One grid will become Government West Virginia has 3 members in the U.S. House of completely shaded and the part Representatives. There are a total of 435 representatives. What percent greater than 100 will be shaded in of the representatives are from West Virginia? Round to the nearest the second grid. hundredth of a percent. 2 EXAMPLE Teaching Tip West Virginia representatives = 3 d total number of representatives 435 Write the fraction. Remind students that they can = 0.0068965517 d Use a calculator. write zeros to the right of decimals without changing the < 0.69% d Write as a percent, and round. value of the decimals. Encourage About 0.69% of the representatives are from West Virginia. students to insert these zeros before moving the decimal point. Check Understanding 4 Idaho has two members in the U.S. House of Representatives. Find the PowerPoint percent of the representatives that are from Idaho. Round to the nearest Additional Examples hundredth of a percent. 0.46%

Write each percent as a decimal and a fraction in simplest form. 2 1 140% 1.40; 15 For more practice, see Extra Practice. 3 EXERCISES 2 0.75% 0.0075; 400 Write each fraction or decimal as a Write each percent as a decimal and as a fraction in simplest form. percent. When necessary, round to A Practice by Example the nearest hundredth of a 4 1.3; 1 3 3 Example 1 1. 180% 1.8; 15 2. 130% 10 3. 175% 1.75; 14 percent. (page 301) 9 2.4; 22 4.52; 413 2 4. 345% 3.45; 320 5. 240% 5 6. 452% 25 3 a. 43 466.67%b. 2.557 255.7% 1 3 9 1 6 Example 2 7. 0.1% 0.001; , 8. 0.75% 0.0075; 9. 0.09% 0.0009; 4 a. 325 0.31% b. 875 0.69% 1 000 400 10,000 (page 301) 1 1 1 10. 0.16% 0.0016; 625 11. 0.5% 0.005; 200 12. 0.05% 0.0005; 2,000 Closure

• How do you write a percent greater than 100 as a mixed 302 Chapter 6 Percents number? Sample: Rewrite the percent as a fraction with denominator of 100, simplify, Reaching All Students and write the improper fraction as a mixed number. Below Level To change percents less Advanced Learners Change each to Visual Learners • How do you write a percent than 1 into fractions, review place a decimal. Place in order from least See note on page 302. greater than 100 or less than 1 values with students. “Count off” the to greatest. If necessary, round to Error Prevention 7 as a decimal? Move the decimal decimal places (tenths, hundredths, the nearest hundredth. 400 0.0175 See note on page 303. 3 point two places to the left. thousands) and write the correct 0.08% 0.000825 2.60 6.2% 0.062 302 number as the denominator. 0.0008, 0.0175, 0.062, 2.60 Write each number as a percent. When necessary, round to the nearest hundredth of a percent. 3. Practice 3 3 1 475% 160% 101% Example 3 13.44 14.15 15. 1100 (page 302) Assignment Guide 29 7 3 16.2 258% 17.3 335% 18. 2 237.5% 50 20 8 1 Objective 1 19. 1.034 103.4% 20. 2.65 265% 21. 4.81 481% A B Core 1–31, 32–37 7 1 3 C Extension 38 –52 Example 4 22.1,000 0.7% 23.400 0.25% 24. 500 0.6% (page 302) Test Prep 53–56 25.7 0.70% 26.5 0.73% 27. 2 0.61% 998 684 329 Mixed Review 57–68 28. 0.00675 0.68% 29. 0.0028 0.28% 30. 0.0001 0.01% Error Prevention! 31. Reading A library ﬁnds that borrowing reference books between 9 libraries is1 10 of what it was 15 years ago. Write this fraction as a Exercises 13–18 Watch for percent. 190% students who add the whole number part and the numerator B Write each percent as a decimal and a fraction. before dividing. 33 32. Sales Jewelry sales in December were 166% of sales in November. 32. 1.66; 150 33. Weather On March 1, the snowpack in the Northern Great Basin of 13 GPS 1.26; 1 Nevada was 126% of the average snowpack. 50 Practice 6-3 Percents Greater Than 100 or Less Than 1 Classify each of the following as: (A) less than 1%, (B) greater than 34. Environment Some studies indicate that the desert shrublands could 100%, or (C) between 1% and 100%. 1 (C)4 (B)2 (A)3 (C) 1.2 2.3 3.300 4. 10 (B) (C) (B) (C) increase as much as 185% in the next century due to global warming. 5. 10.8 6. 0.7 7. 1.4 8. 0.06

17 9. 1.03 (B)10. 0.009 (A)11. 0.635 (C)12. 0.0053 (A) 1.85; 120 .to compare the numbers in each pair ؍ Use S , R , or 35–37. See margin. 1 SRRR1 3 Model each percent using one or more 10 3 10 grids. 13. 4 20% 14. 2% 50 15. 0.008 8% 16. 35% 8 SR 7 ؍ S 5 17. 150% 4 18. 3 300% 19. 250 0.3% 20. 650% 7 35. 175% 36. 120% 37. 0.5% Write each fraction or decimal as a percent. Round to the nearest tenth of a percent if necessary. 7 140%137 137%0.8 0.8% 21.5 22.100 23. 100 21 525%17 170%65 162.5% 24.4 25.10 26. 40 Write each number as a percent. 37 185%7 1.4%9 112.5% 27.20 28.500 29. 8 6 51 3 15 Write each decimal as a percent. 38.120% 39. 1.55 40.204% 41.1 175% 42. 187.5% 0.3% 180% 0.25% 5 25 4 8 30. 0.003 31. 1.8 32. 0.0025 155% 33. 5.3 530%34. 0.0041 0.41%35. 0.083 8.3%

36. 0.0009 0.09%37. 0.83 83%38. 20 2,000%

Decide whether each percent is reasonable. Explain why or why not. Write each percent as a decimal and as a fraction in simplest form. 1.75; 13 1.2; 11 0.004, 1 4 5 2 250 39. 175% 40. 120% 41. 5% 0.00625, 1 7.5; 71 0.0825, 33 43. Buttermilk is 105% milk fat. No; it cannot be more than 100% milk fat. 5 160 2 1 400 42. 8% 43. 750% 44. 8 4% 45. In 1990, the population of Kansas was 2,477,574, which included 21,965 Native Americans. What percent of the people living in 44. Rainfall in Oklahoma this year is reported to be 120% of the average. Kansas were Native Americans? Yes; the rainfall can be 1.2 times the average. about 0.89% 1 46. The mass of Earth is 318 of the mass of Jupiter. What percent is this? 45. A scientiﬁc study concluded that 0.5% of the seeds will not grow. about 0.31% 47. If you surpass the goal Yes; it is reasonable that 1 of 1% of the seeds did not grow. 1 2 by 5 of the amount of 46. The addition raised the school’s value to 0.7% of its previous value. the goal, then you have No; “raising” the value would make it more than 100% of the prior value. 1 Reteaching 6-3 Percents Greater Than 100 or Less Than 1 reached 15 of the goal, 47. Writing in Math What does it mean to reach 120% of a savings goal? You can express a percent that is less than 1% or greater than 100% or 120% of the goal. as a decimal and as a fraction. A percent that is less than 1% is a See left. 1 quantity that is less than 100 . A percent that is greater than 100% is a quantity that is greater than 1. C Write each percent as a decimal. See left. • Write 0.5% as a decimal and as a fraction. 2.10175 Move the decimal point two places to the left to 00.5% 0.005 1 3 5 7 write a percent as a decimal. Add zeros as needed. 0.5 50. 1.90714285, or 48.%1.52125 49.%152 50.%114 51. 210 %190 Since percent means per 100, you can write the 0.5% 100 8 16 7 40 percent as a fraction with a denominator of 100. about 1.191 1.141875 Then rewrite the numerator as a whole number. 0.5 0.5 3 10 5 1 100 5 100 3 10 5 1,000 5 200 Since 10 0.5 5, multiply the numerator and the 52. Auctions Recently, a near-mint copy of the Baltimore Orioles 1966 denominator by 10. Then simplify. 1 So, 0.5% 0.005 200. Yearbook was auctioned for $15. The yearbook cost $.50 in 1966. Write • Write 125% as a decimal and as a fraction. Move the decimal point two places to the left to 125% 1.25. a ratio of the auction price to the original price. Find the percent. write a percent as a decimal. Add zeros as needed. Since percent means per 100, you can write the 125 15 150 125% 100 , or , or 30; 3,000% percent as a fraction with a denominator of 100. 0.5 5 125 125 4 25 5 1 Then simplify. 100 5 100 4 25 5 4 5 14 So, 125% 1.25 11. 6-3 Percents Greater Than 100% or Less Than 1% 303 4 Write each percent as a fraction and a decimal. 1. 0.01% 2. 0.45% 1 ; 0.0001 9 ; 0.0045 35. Use the Guided Problem 10,000 2,000 3. 0.2% 4. 0.67% 1 ; 0.002 67 ; 0.0067 GPS Solving worksheet with 500 10,000 Exercise 33. 5. 150% 6. 225% 3 11; 1.5 9 21; 2.25 2 5 2 4 5 4 36–37. See back of book. 7. 186% 8. 201% 93 143; 1.86 201 2 1 ; 2.01 50 5 50 100 5 100

303 4. Assess Test Prep

Multiple Choice 53. Which set of numbers represents the shaded PowerPoint Lesson Quiz 6-3 area of the ﬁgure at the right? D Write each as a decimal and a A. 0.38%, 38 , 0.038 B. 3.8%, 38 , 0.38 100 100 fraction or mixed number in C. 38%, 38 , 0.038 D. 38%, 38 , 0.38 simplest form. 100 100 3 9 1. 112% 1.12; 125 Take It to the NET 54. The fraction 1,000 is equal to which set of numbers? F 1 Online lesson quiz at F. 0.9%, 0.009 G. 0.9%, 90 H. 9%, 0.9 I. 90%, 0.90 2. 0.8% 0.008; 125 www.PHSchool.com Web Code aba-0603 Write each as a percent. 55. One hour is what percent of one week? Round to the nearest tenth. B 1 A. 0.5% B. 0.6% C. 5.9% D. 6.0% 3. 32 350% 4. 0.0045 0.45% Short Response 56. You miss 1 day of school out of 180 days in the school year. a. Explain how to express 1 day out of school as a percent. Alternative Assessment b. Round to the nearest tenth of a percent. See margin.

Each student in a pair writes two percents greater than 100 and two percents less than 1. Partners Mixed Review exchange papers and write each percent as a decimal and as a Lesson 6-2 Write each percent as a fraction in simplest form. fraction. Then partners work 7 3 4 37 together to arrange the eight 57. 28% 25 58. 37.5% 8 59. 80% 5 60. 74% 50 original percents in order from 19 1 19 3 least to greatest. 61. 19% 100 62. 10% 10 63. 95% 20 64. 3% 100

Test Prep Lesson 4-4 Find each product. 65. 3 ? 40 24 66. 5 ? 144 80 67. 7 ? 280 245 68. 1 ? 423 70.5 Resources 5 9 8 6 For additional practice with a variety of test item formats: • Test-Prep, p. 341 Practice Game • Test-Taking Strategies, p. 337 Order, Please! • Test-Taking Strategies with Transparencies What You’ll Need Exercise 55 Elicit the fact that • 30 pieces of construction paper, each with a fraction, decimal, or a there are 168 hours (24 x 7) in one percent written on it. Include mixed numbers or the equivalent week. decimals and percents.

How to Play Enrichment 6-3 Percents Greater Than 100 or Less Than 1 • Select two teams of ﬁve players. Each player receives one piece Critical Thinking

Answer the questions with the information given. of construction paper. 1 A small percent of bats carries rabies—generally, about 2 %. In how large a group of bats would you expect to find exactly one bat • When play begins, team members must order themselves carrying rabies? Explain how you found your answer. 1 about % 1. What percent of bats carries rabies? 2 0.5 from the least to the greatest numbers. 1 100 2. Write 2 % as a fraction. • The ﬁrst team to order their numbers correctly is the winner 3. Write your fraction from Exercise 2 with a whole number in the . numerator. 5 1,000

4. Explain what your fraction means by giving the number of bats that may have rabies and the group size. Sample answer: About 5 bats in a group of 1,000 bats have rabies.

5. Write a fraction with a numerator of 1 equivalent to the fraction you wrote in Exercise 3. 1 200

6. About how large would you expect a group of bats to be if one bat carries rabies? 304 Chapter 6 Percents 200 bats

7. Explain how you found your answer. 1 Sample answer: Write2 % as a fraction. Then 56. [2]a. Divide 1 by the total answer only find an equivalent fraction with a numerator of 1. number of school days, 8. Does your answer mean that every group of bats this size will have exactly one bat with rabies? Explain. 180. Sample answer: No, it is only an average. 1 Some groups will have more than one rabid b. 180 5 0.00555 . . . bats and others will have none. N 0.555% N 0.6% [1] minor error OR 304