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

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Algebra 2-1 Rational Numbers on a Number Line

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Presentation transcript:

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

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?

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

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…

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

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

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

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

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

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

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

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

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

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

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

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?

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

Homework P. 67 #18-56E