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Name ________________________________________ Date __________________ Class __________________ LESSON 1-1 Rational and Irrational Numbers Practice and Problem Solving: D Write each fraction as a decimal. The first one is done for you. 1. 1 9 2. 0.1 ________________________ 11 20 3. _______________________ 9 16 ________________________ Write each decimal as a fraction. The first one is done for you. 4. 0.258 5. 4.8 258 129 = 1000 500 ________________________ 6. 0.333 _______________________ ________________________ Find the two square roots of each number. The first one is done for you. 7. 16 8. 49 4, −4 ________________________ 9. _______________________ 25 4 ________________________ Find the cube root of each number. The first one is done for you. 10. 343 11. 1 7 × 7 × 7 = 343, 7 ________________________ 12. _______________________ 8 27 ________________________ Approximate each irrational number to the nearest hundredth without using a calculator. The first one is done for you. 13. 32 5.66 ________________________ 14. 15. 59 _______________________ 118 ________________________ Solve. 17 square 100 mile. What is Vatican City’s area written as a decimal? 16. The world’s smallest country is Vatican City. It covers _________________________________________________________________________________________ 17. A square sandbox has an area of 25 ft2. What is the length of each of its sides? (Hint: side = 25 ) _________________________________________________________________________________________ Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 3 UNIT 1: Real Numbers, Exponents, and Scientific Notation Practice and Problem Solving: C MODULE 1 Real Numbers 1. 1.17 in. LESSON 1-1 2. 7.64 in. Practice and Problem Solving: A/B 41 9 = 0.82, = 0.81, and 50 11 10 41 9 = 0.90 , 0.81 is closer to . 50 11 11 3. Since 1. 0.125 2. 0.5625 3. 0.55 4. 5.32 4. ± 1 2 5. ± 1 4 5. 0.93 6. 2.583 7. 0.03 6. ≈ ± 8. 3.2 9. 5, −5 7. ≈ 1.73 10. 1, −1 8. ≈ 4.24 5 5 11. , − 2 2 12. 2 3 11 11 ,− 7 7 9. When you find a square root, you find two factors that are the same. They can be positive or negative. When you find a cube root, you find three factors that are the same. They are positive. 13. 2 14. 5 15. 1 10. The length of one photo album page is 25 cm. The width of the page is 32 cm. 16. 13 17. 5.66 Practice and Problem Solving: D 18. 10.86 19. 4.24 1. 0.1 20. 17.86 2. 0.55 21. 2.83 3. 0.5625 4. 22. 8.66 129 500 5. 4 23. 1.4 lb 6. 24. 288 in2 4 5 333 1000 7. 4, −4 8. 7, −7 Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 322 9. Success for English Learners 5 5 ,− 2 2 1. 10. 7 2. Possible answer: If you have a square with a side length of 5, then 52 is how you find the area of that square. 11. 1 12. 1 = 0.25 4 2 3 3. Because the answer is an approximation. 13. 5.66 14. 7.68 LESSON 1-2 15. 10.86 Practice and Problem Solving: A/B 16. 0.17 mi2 1. real, rational 17. 5 ft 2. real Reteach 3. real, rational, integer 1. 3.75 4. real, rational, integer 2. 0.83 5. real, rational 3. 3.6 6. real, rational, integer, whole 4. 9, −9 7. false; irrational real numbers include nonterminating decimals 5. 7, −7 6. 8. true 5 5 ,− 6 6 9. rational; all money amounts can be written as fractions 7. 3 8. 5 10. real numbers; the temperature can be any number between 0 and 100 degrees Celsius 9. 9 11. rational 6< 39 < 7 12. integers Reading Strategies 13. irrational 1. Yes, because it can be written as a fraction: 0.62 = 62 = 31 . 100 50 14. whole numbers Practice and Problem Solving: C 2. No, because it cannot be written as a decimal that terminates or repeats. 1. real 2. real, rational, integer 3. Yes, as long as the decimal is infinite and nonrepeating, such as 0.31311311131111…. 3. real, rational 4. real, rational, integer, whole 4. Yes, for example, 0.6 . 5. real, rational 5. A decimal that is an irrational number is infinite and nonrepeating, such as the value for π. 6. real, rational, integer, whole 7. integers; possible points are positive and negative numbers 6. Both are real numbers and both can be written as decimals. 8. real; elevation can be any number above or below zero 9. no; there are an infinite number of rational numbers between any two integers Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor. 323