1. 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.
Then/Now

3. Concept

4. Classify Real Numbers
A. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.
Answer: This decimal is a rational number because its digits repeat. It is equivalent to
Example 1 A

5. Classify Real Numbers
B. Name all of the sets of numbers to which the real number belongs. Write whole, integer, rational, or irrational.
Answer: Since this number is a whole number, an integer, and a rational number.
Example 1 B

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

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

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

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

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

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

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

13. Compare Real Numbers
Example 2

14. A. <
B. >
C. =
D. none of the above
Example 2 CYP

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

16. Order Real Numbers
Example 3

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

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

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

20. A. Solve the equation m2 = 81. Round to the nearest tenth, if necessary.
B. 8 and –8
C. 9
D. 9 and –9
Example 4 CYP A

21. B. Solve the equation h2 = 24. Round to the nearest tenth, if necessary.
A. 4.8 and –4.8
B. 4.9
C. 4.9 and –4.9
D. 5 and –5
Example 4 CYP B

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

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

24. A. 7.1 ft
B. 9.9 ft
C. 14 ft
D. 98 ft
Example 5

25. End of the Lesson