Download Essential Questions: What is an irrational number? Videos: What is a

August 30, 2016
Essential Questions:
1. How do you compare real numbers?
2. What is a conditional statement?
3. What is absolute value?
Videos:
What is a rational number?
What is an irrational number?
Whole Numbers
-Whole numbers are the numbers 0, 1, 2, 3, .....
- Numbers are "whole" and not "parts of"
(or decimals)
Integers
-Integers are like whole numbers but also
include the negative of the whole numbers.
-Still no fractions (or decimals) allowed!
August 30, 2016
Rational Numbers
-any number that can be written as a fraction
-this includes whole #'s and decimals that can be written as
fractions
Number
As a fraction
Rational???
7
.33 (terminating
decimals)
6/7
√9
repeating decimals
Ex. 0.121212121....
Irrational Numbers
-decimals that go on and on forever without repeating
"non-terminating, non-repeating decimals"
Examples:
2.12345678987654387167261536484993615379...
Square roots of non-perfect squares Ex. √2, √11, √18,etc.
π, e
August 30, 2016
Real Numbers
-In Algebra 1, any number you can think of is a
real number
-FYI - When you get into Algebra 2 you will learn
about numbers that are not real. These
numbers are called imaginary numbers.
Real
Irrational
11
-6 1
2
-1.2
-8 -7 -6 -5 -4 -3 -2 -1
Ra-9 tional
3.5
2
(or decimals)
Square root of
non perfect
squares
ex. √7, √3, √22
In-9tegers
-8 -7 -6 -5 -4 -3 -2 -1
Whole
(or decimals)
(or decimals)
Non-terminating/
non-repeating
decimals
ex. π, e,
4.98475410...
August 30, 2016
Summary:
Fill in the table:
Number
5
.12
2/3
Nonterminating
nonrepeating
decimal
√16
√8
π
-4
Whole
Integer
Rational
Irrational
Real
August 30, 2016
Ordering Rational Numbers
The further left, the smaller the number
The further right, the larger the number
Compare with an inequality sign (> or <)
-4 ___ -2
0 ___ 3
5 ___ -3
0.9 ____0.89
-2 ___ -1
0 ___ -6
3 ___ 5
-0.3 ___ -0.31
-12 ___ -1
-2.13 ___ -2.03
-7 ___ -120
-300 ___ 90
√5 ___ 2/3
-7/8 _____-2 1/2
π ___ 3.142
8.123 ____ √65
30/4 ____ √49
15/2 ____ 7.51
Fill in the chart
#'s may be used in more than one box
Numbers
8, -3.2, -5, 1/2
2.3, -4/3,
-2.1, 0
-3/4, -1.4, √12
5, 0.6, -2 2/3
Which #'s
Which #'s Which #'s Write the #'s from least to
are whole
are integers are rational greatest
#'s
August 30, 2016
Opposite Numbers
-Two numbers that are the same distance from
zero on a number line are called "opposites"
Number
Opposite
-8
1 2/3
-0.92
a
Absolute Value
-The (positive) distance a number is away
from zero
-Symbol: |
|
-How it is read: |6| = "the absolute value of 6"
| -4 | = 4
|4|=4
-Treat the abs. value bars like parenthesis
ie. Do any calculations inside the bars first
Then take the absolute value of the ans.
August 30, 2016
For the given value of x, find -x and | x |
Opposites
x
-x
|x|
4
-9
0
-1.45
-3/5
Find the absolute value. Remember....treat
the abs. value signs like ( )
| 9 - 7 | + 10
5
2
| 2⋅3 + 10 | - 4
-
5
7
| 3.2 - 1.2 |
August 30, 2016
Keystone Exam "trick" problems
If x is positive, then | x | =
ex.
If x is zero, then | x | =
ex.
If x is negative, then | x | =
ex.
Conditional Statement
-has a hypothesis ("if" part of an if-then statement)
-has a conclusion ("then" part of an if-then statement)
-a conditional statement can be either true or false
-true....only if always true
-if false for one example, then the entire statement
is false
Ex. If a figure is a square, it has four sides.
-Since every square has four sides, this statement
would be true
Ex. If a figure has four sides, it is a square.
-A rectangle has 4 sides
-Only one "counterexample" is needed to say a
statement is false
August 30, 2016
Underline the hypothesis and circle the conclusion.
Tell whether the statement is true or false.
If true, do nothing else.
If false, give a counterexample.
1. If a number is a whole number, then it is a real number.
2. If a number is a real number, it is a whole number.
Tell whether the statement is true or false.
If true, do nothing else.
If false, give a counterexample.
1. If 2 + 3 = 5, then 3 + 2 = 5.
2. If 7 - 5 = 2, then 5 - 7 = 2.
3. If 7 ⋅ 6 = 42, then 6 ⋅ 7 = 42
4. If 10 ÷ 5 = 2, then 5 ÷ 10 = 2.
August 30, 2016
Tell whether the statement is true or false.
If false, give a counter example.
1. If a number is negative, it is an integer.
2. If x is a positive number, its absolute value is negative.
3. If a number is negative, its opposite is positive.
4. If a number is rational, it is zero.
5. If given a number x, then -x is negative.
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