1. Warm-Up
Classify each number below in as many ways as possible -4
7.89

2. Warm-Up What is a number line?
What do you need to make sure you include on a number line?
What could you use a number line for?

3. Section 2.1: The Real Number Line
SWBAT graph and compare real numbers using a number line
SWBAT find the opposite and absolute value of a real number

4. Types of Real Numbers Natural Numbers: 1,2,3,4,5… Whole Numbers:
0,1,2,3,4…
Integers:
…-3,-2,-1,0,1,2,3…

5. Types of Real Numbers Rational Numbers:
A decimal that terminates or repeats. Any number that can be written as a fraction
Examples: ⅓, ⅛, 0.5, -5, 0.3
Irrational Numbers:
Any number that cannot be represented as a fraction. Any decimal that goes on forever with no pattern.
Examples: √2, √3, ℮, π

6. Example Classify the numbers below in as many ways as possible 9 -3
5.67 e

7. The Real Number Line
We can represent real numbers on a real number line.
Negative #s
Positive #s
Origin

8. Example
Plot 4, 3/2, and -2.6 on the number line
-2.6
3/2 4 -1 1

9. Comparing Real Numbers
The further to the left a point is on the number line, the smaller it is.

10. Example
Graph -6.4 and -6.7 on the number line. Then write two inequalities comparing these numbers.

11. Example Write the numbers in increasing order
4.66, 0.7, 4.6, -1.8, 3, -0.66

12. Opposites
Two numbers are opposites that are the same distance from zero on the number line but on opposite sides.
Example:
The opposite of 5 is -5

13. Absolute Value
The absolute value of a number is equal to its distance from zero on a number line
Ex: Both 3 and -3 are 3 units from zero.
Both have an absolute value of 3.
|3|=3
|-3|=3
Called Absolute Value Bars

14. Example
Solve the equation:
| x | =4
y = |-9.6|

15. Velocity
Velocity indicates both speed and direction (up is positive and down is negative).
The speed of an object is the absolute value of its velocity

16. Example (p. 66 ex #8)
A space shuttle launch pad elevator drops at a rate of 10 ft per second. What are its velocity and speed?

17. Counterexample
A counterexample is an example that proves a statement is false.

18. Homework
P. 67 #18-56E