Transcript Section 2.1: The Real Number Line

Warm-Up
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Classify each number below in as many ways
as possible
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
-4
7.89
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7
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9
0
Warm-Up
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
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…
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Whole Numbers:
0,1,2,3,4…
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Integers:
…-3,-2,-1,0,1,2,3…
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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
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Irrational Numbers:
Any number that cannot be represented as a
fraction. Any decimal that goes on forever with
no pattern.
Examples: √2, √3, ℮, π
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Example
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Classify the numbers below in as many
ways as possible
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9
-3
5.67
e
The Real Number Line
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We can represent real numbers on a real
number line.
Negative #s
Positive #s
0
Origin
Example
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Plot 4, 3/2, and -2.6 on the number line
-2.6
3/2
-1 0 1
4
Comparing Real Numbers
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The further to the left a point is on the
number line, the smaller it is.
Example
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Graph -6.4 and -6.7 on the number line.
Then write two inequalities comparing
these numbers.
Example
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Write the numbers in increasing order
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4.66, 0.7, 4.6, -1.8, 3, -0.66
Opposites
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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
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Absolute Value
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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
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Example
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Solve the equation:
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| x | =4
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y = |-9.6|
Velocity
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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)
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A space shuttle launch pad elevator drops
at a rate of 10 ft per second. What are its
velocity and speed?
Counterexample
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A counterexample is an example that
proves a statement is false.
Homework
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P. 67 #18-56E