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# The Real Number System

The Real Number System. Real Numbers. The set of all rational and the set of all irrational numbers together make up the set of real numbers. Any and all kinds of numbers fall under real numbers. Rational Numbers.

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## The Real Number System

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1. The Real Number System

2. Real Numbers • The set of all rational and the set of all irrational numbers together make up the set of real numbers. • Any and all kinds of numbers fall under real numbers.

3. Rational Numbers Rational numbers are numbers that can be written as fractions. That is, the form a/b where a and b are both integers and b ≠ 0.

4. -6 8 2/5 .05 -2.6 5.3333333 -8.12121212… √16 Examples of Rational Numbers

5. Irrational Numbers • Irrational Numbers – numbers that are not repeating or terminating decimals. • Examples: • .01001000100001… • √2 = 1.414213562… • 3.14159…

6. Whole Numbers, Natural Numbers, and Integers • Whole Numbers include the following: • 0,1,2,3,4,5,6,7,8,9,10,….. • Natural Numbers include the following: • 1,2,3,4,5,6,7,8,9,10,….. Does not include 0. • Integers include the following: • …-3,-2,-1,0,1,2,3,…

7. Classifying Real Numbers • Directions: Classify the following numbers as natural, whole, integer, rational, and/or irrational.

8. 8 • This number is a natural number, a whole number, an integer, and a rational number. • 0.33333 • This repeating decimal is a rational number because it is equivalent to 1/3. • √17 • √17 = 4.123105… It is not the square root of a perfect square so it is irrational.

9. -28/2 • Since -28/4 = -14, this number is an integer and a rational number. • -√121 • Since -√121 = -11, this number is an integer and a rational number.

10. Solving Equations • a2 = 49 • To undo the square, take the square root of both sides. Then, you have this. • √a2 = √49 • a = √49 or a = -√49 • a = 7 or a = -7 • Hence, the solutions are 7 and -7.

11. d2 = 55 • Take the square root of both sides. • √d2 = √55 • d = √55 or d = - √55 • d = 7.41 or d = - 7.41 • Hence, the solutions are 7.41 and -7.41.

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