1. Absolute Value Find the absolute value of a number Just how far from zero are you?

2. Absolute Value Absolute value of a number is the DISTANCE to ZERO.Absolute value of a number is the DISTANCE to ZERO. Remember distance itself is ALWAYS positive -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

3. Be careful! In math a negative sign in front of the absolute value sign should be read “take the opposite of”. This means treat the absolute value sign like a grouping symbol. Do the work inside first THEN take the opposite of

4. Opposites Two numbers that have the same ABSOLUTE VALUE, but different signs are called opposite pairs. (Zero Pairs) Example -6 and 6 are opposite pairs (Zero Pairs) because both are 6 units away from zero. | -6 | = 6 and | 6 | = 6 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6

5. Using Absolute Value in Real Life The graph shows the position of a diver relative to sea level. Use absolute value to find the diver’s distance from the surface.

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

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

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

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

10. Rational Numbers Rational numbers are any numbers that can be expressed in the form of, where a and b are integers, and b ≠ 0. They can always be expressed by using terminating decimals or repeating decimals.

11. Terminating Decimals Terminating decimals are decimals that contain a finite number of digits. Examples:  36.8  0.125  4.5

12. Repeating Decimals Repeating decimals are decimals that contain a infinite number of digits. Examples:  0.333…   7.689689… FYI…The line above the decimals indicate that number repeats.

13. Venn Diagram of the Real Number System Rational Numbers

14. To show how these number are classified, use the Venn diagram. Place the number where it belongs on the Venn diagram. Rational Numbers Integers Whole Numbers Natural Numbers 117 0 6.36 -3

15. Solution Now that all the numbers are placed where they belong in the Venn diagram, you can classify each number: –117 is a natural number, a whole number, an integer, and a rational number. – is a rational number. –0 is a whole number, an integer, and a rational number. –-3 is an integer and a rational number. –6.36 is a rational number. – is an irrational number.