Download Section 2.1: The Real Number Line

Warm-Up

Classify each number below in as many ways
as possible


-4
7.89

7


9
0
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
0
Origin
Example

Plot 4, 3/2, and -2.6 on the number line
-2.6
3/2
-1 0 1
4
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.
Called
|3|=3
Absolute
Value
|-3|=3
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