1. Warm Up Add or subtract. 1 + – 1515 1 1. 2525 2. 7 12 3 – 2 3. 6.5 + –1.2 4. 3.4 – 0.9 5.3 2.5 3535 11 12 1313 1

2. The Real Number System

3. A real number is basically a number that is somewhere on a number line. The Real Number System is divided into two categories: Rational and Irrational.

4. A rational number is any number that can be written as a fraction, where n and d are integers and d  0. n d

5. Fractions are rational numbers. Decimals that terminate or repeat are rational numbers. Whole numbers are rational numbers. Integers are rational numbers. 0 is a rational number.

6. An Irrational Number is a number that cannot be written as a simple fraction - the decimal goes on forever without repeating. It is called irrational because it cannot be written as a ratio (or fraction), not because it’s crazy!

7. π (Pi) is an irrational number. The value of Pi is 3.14159265358979323846264 3383279 (and more...) There is no pattern to the decimals, and you cannot write down a simple fraction that equals Pi.

8. Square roots of non-perfect “squares” are irrational. For example, is irrational.

9. Real numbers consist of all the rational and irrational numbers. The real number system has many subsets: –Natural Numbers –Whole Numbers –Integers

10. Natural numbers are the set of counting numbers. {1, 2, 3,…}

11. Whole numbers are the set of numbers that include 0 plus the set of natural numbers. {0, 1, 2, 3, 4, 5,…}

12. Integers are the set of whole numbers and their opposites. {…,-3, -2, -1, 0, 1, 2, 3,…}

13. Real Numbers Rational NumbersIrrational Numbers 3 1/2 -2 15% 2/3 1.456 -0.7 0 33 22 -  5 2 3434

14. Real Numbers Rational NumbersIrrational Numbers 3 1/2 -2 15% 2/3 1.456- 0.7 33 22 -  5 2 3434 Integers

15. Real Numbers Rational NumbersIrrational Numbers 3 1/2 -2 15% 2/3 1.456- 0.7 33 22 -  5 2 3434 Integers Whole

16. Real Numbers Rational NumbersIrrational Numbers 3 1/2 -2 15% 2/3 1.456- 0.7 0 33 22 -  5 2 3434 Integers Whole Natural

17. System

18. Where do these numbers belong? 0, ½, -3, , 117, 6.36,.3,

19. 0 117 -3 1/2 6.36.3  System