1. The Real Numbers 4-7 Learn to determine if a number is rational or irrational.

2. The Real Numbers 4-7 Recall that rational numbers can be written as fractions. Rational numbers can also be written as decimals that either terminate or repeat. 3 = 3.8 4545 = 0.6 2323 1.44 = 1.2

3. The Real Numbers 4-7 Irrational numbers can only be written as decimals that do not terminate or repeat. If a whole number is not a perfect square, then its square root is an irrational number. 2 ≈1.4142135623730950488016… A repeating decimal may not appear to repeat on a calculator, because calculators show a finite number of digits. Caution!

4. The Real Numbers 4-7 The set of real numbers consists of the set of rational numbers and the set of irrational numbers.

5. The Real Numbers 4-7 Example 1: Classifying Real Numbers Identify as rational or irratioanl. 5 irrational –12.75 is a terminating decimal. –12.75 rational 16 2 rational = = 2 4242 16 2 A. B. C.

6. The Real Numbers 4-7 Example 2 Write all names that apply to each number. 9 rational –35.9 is a terminating decimal. –35.9 rational 81 3 rational = = 3 9393 81 3 A. B. C. 9 = 3

7. The Real Numbers 4-7 State if each number is rational, irrational, or not a real number. 21 irrational 0303 rational 0303 = 0 Example 3: Determining the Classification of All Numbers A. B.

8. The Real Numbers 4-7 not a real number Example 4: Determining the Classification of All Numbers –4 4949 rational C. D. State if each number is rational, irrational, or not a real number.

9. The Real Numbers 4-7 23 irrational 9090 undefined, so not a real number Example 5 A. B. State if each number is rational, irrational, or not a real number.

10. The Real Numbers 4-7 not a real number –7 64 81 rational C. D. Example 6 State if each number is rational, irrational, or not a real number.

11. The Real Numbers 4-7 The Density Property of real numbers states that between any two real numbers is another real number. This property is also true for rational numbers, but not for whole numbers or integers. For instance, there is no integer between –2 and –3.

12. The Real Numbers 4-7 Example 7: Applying the Density Property of Real Numbers 2525 3 + 3 ÷ 2 3535 There are many solutions. One solution is halfway between the two numbers. To find it, add the numbers and divide by 2.5 = 6 ÷ 2 1212 = 7 ÷ 2 = 3 3 1212 333 1515 2525 433 3535 4545 Find a real number between 3 and 3. 3535 2525 A real number between 3 and 3 is 3. 3535 2525 1212

13. The Real Numbers 4-7 Standard Lesson Quiz Lesson Quizzes Lesson Quiz for Student Response Systems

14. The Real Numbers 4-7 Lesson Quiz Write all names that apply to each number. 1. 2. – State if each number is rational, irrational, or not a real number. 3. 4. Find a real number between –2 and –2. 3838 3434 5. 2 4 9 16 2 25 0 not a real number rational irrational rational Possible answer –2. 5858

15. The Real Numbers 4-7 1. Identify rational, irrational, not real. A. irrational B. rational C. Not real D. All of the above Lesson Quiz for Student Response Systems

16. The Real Numbers 4-7 2. Identify the name that applies to. A. irrational B. rational C. not a real number D. none Lesson Quiz for Student Response Systems

17. The Real Numbers 4-7 3. Identify a real number between. A. –4 B. C. D. Lesson Quiz for Student Response Systems