1. Then/Now You have already compared fractions and decimals. (Lesson 3–1) Identify and compare numbers in the real number system. Solve equations by finding square roots.

2. Vocabulary irrational numbers real numbers

3. Concept

4. Number sets 1.Natural numbers 2.Whole numbers 3.Integers 4.Rational numbers 5.Irrational numbers

5. How the number sets are related

6. Example 1 A Classify Real Numbers A. Name all of the sets of numbers to which the real number 0.246 belongs. Write whole, integer, rational, or irrational.

7. Example 1 B Classify Real Numbers B. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.

8. Example 1 C Classify Real Numbers C. Name all the sets of numbers to which the real number –7.25 belongs. Write whole, integer, rational, or irrational.

9. Example 1 D Classify Real Numbers D. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.

10. A.A B.B C.C D.D Example 1 CYP A A. Name all the sets of numbers to which the real number 0.380 belongs. Write whole, integer, rational, or irrational.

11. A.A B.B C.C D.D Example 1 CYP B B. Name all the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.

12. A.A B.B C.C D.D Example 1 CYP C C. Name all the sets of numbers to which –2.25 belongs. Write whole, integer, rational, or irrational.

13. Example 2 Compare Real Numbers Express each number as a decimal. Then compare the decimals.

14. A.A B.B C.C D.D Example 2 CYP

15. Example 3 Order Real Numbers Express each number as a decimal. Then order the decimals.

16. Example 3 Order Real Numbers

17. A.A B.B C.C D.D Example 3 CYP

18. Example 4 A Solve Equations A. Solve w 2 = 169. Round to the nearest tenth, if necessary. w 2 =169Write the equation. Answer: The solutions are 13 and –13. Definition of square root. w=13 or w = –13

19. Example 4 Solve Equations B. Solve r 2 = 50. Round to the nearest tenth, if necessary. r 2 =50Write the equation. Answer: The solutions are approximately 7.1 and –7.1. Definition of square root. Use a calculator.

20. A.A B.B C.C D.D Example 4 CYP A A. Solve the equation m 2 = 81. Round to the nearest tenth, if necessary.

21. A.A B.B C.C D.D Example 4 CYP B B. Solve the equation h 2 = 24. Round to the nearest tenth, if necessary.

22. Example 5 Use Real Numbers to Solve Problems Write the formula. Replace R with 6.4 and A with 40.

23. Example 5 Use Real Numbers to Solve Problems Answer: The wingspan is 16 feet. Multiply each side by 40. Consider only the positive square root. Simplify.

24. A.A B.B C.C D.D Example 5