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# The Real Number System

The Real Number System. The Real Number System. Natural Numbers are the counting numbers. i.e. The numbers you NATURALLY count with. 1, 2, 3, 4, 5,. Whole Numbers consists of the natural numbers and zero. 0, 1, 2, 3, 4, 5, . . .

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## The Real Number System

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1. The Real Number System

2. The Real Number System • Natural Numbers are the counting numbers. • i.e. The numbers you NATURALLY count with. • 1, 2, 3, 4, 5, . . .

3. Whole Numbers consists of the natural numbers and zero. • 0, 1, 2, 3, 4, 5, . . . • Integers consists of the natural numbers, their opposites, and zero. • . . . -3, -2, -1, 0, 1, 2, 3 . . .

4. Number Line: Whole Numbers Natural Numbers Integers

5. Rational Numbers • Rational Numbers consist of all integers plus terminating and repeating decimals. • Terminating Decimals: decimals that stop. • Examples: 2.5, 0.25, 6.73, 100.993 • Repeating Decimals: decimals that repeat. • Examples: 0.33, 0.67676767…, 0.213213213213…

6. A rational number is any number that can be expressed as the quotient of two integers (fractional form). • For example: 1 2 25 100 2 1 = 0.5 = 0.25 = 2

7. Irrational numbers consist of numbers that CANNOT be expressed as the quotient of two integers. • In decimal form, irrational numbers have neitherterminating or repeating decimals. • For Example: π = 3.14…

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