Download 1-3 Real Numbers and the Number Line

1-3 REAL NUMBERS AND
THE NUMBER LINE
I Can:
-
classify, graph, and compare real
numbers .
-
find and estimate square roots.
VOCABULARY TO KNOW
Square
Root
A
number a is a square root of a
number b if a2 = b
Example:
72 = 49, so 7 is the
square root of 49.
SQUARE ROOT
You
can use the definition of square root
to find the exact square roots of some
nonnegative numbers.
The
radical symbol indicates a
nonnegative square root, that is also
called the principal square root.
VOCABULARY TO KNOW
 Radicand
 The
expression under the radical symbol is
called the radicand.
x
is the radicand in this case
VOCABULARY TO KNOW
Radical
Together,
the radical symbol and
radicand form a radical.
SIMPLIFYING SQUARE ROOT
EXPRESSIONS
 What
is the simplified form of each
expression?
81
9
16
VOCABULARY TO KNOW
 Perfect
 The
Square
square of an integer
 For
this class, you are required to memorize all perfect
squares from 1-144.
 Copy
this list and study it.
12 = 1
72 = 49
22 = 4
82 = 64
32 = 9
92 = 81
42 = 16
102 = 100
52 = 25
112 = 121
62 = 36
122 = 144
ESTIMATING A SQUARE ROOT
Lobster
eyes are made of tiny square
regions. Under a microscope, the
surface of the eye looks like graph
paper. A scientist measured the area of
one of the squares to be 386 square
microns. What is the approximate side
length of the square of the nearest
micron?
TYPES OF NUMBERS
Numbers
can be classified by their
characteristics.
Some
can be represented on the
number line.
SETS
Numbers
Set-
are classified using sets.
a well-defined collection of objects.
 Each
Subset-
object is an element of the set.
consists of elements from the
given set.
Sets of Numbers
natural numbers
{1,2,3,…}
0
whole numbers
{0,1,2,3,…}
0
Integers
{…,-2,-1,0,1,2,…}
0
1
5
3
11
2
Sets of Numbers
5.75


3
4
5

6
7
𝑎
𝑏
• Rational numbers can be written in the form where a
and b are integers. They can also be written in decimal
form.
• Decimals must be terminating or repeating.

Sets of Numbers
15


3
4
5
6
• Irrational numbers cannot be written in as a quotient of
two integers.
• Decimals are non-terminating
• Ex: 0.1010010001…, 3.141592…
7
#1
What kind of number is -5?
integer, rational
#2
What kind of number is
42?
natural, whole, integer,
rational
#3
What kind of number is -4.5669?
rational
#4
Give an example of a whole number that isn’t
positive.
REAL NUMBERS
Rational
numbers and irrational numbers form the set
of real numbers.
Subsets
of real numbers:
Natural
Whole
Integer
Rational
Irrational
Inequalities
An inequality is a mathematical sentence comparing the
values of two expressions using an inequality symbol.
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
8
>
-6
Inequalities
-9 -8 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8
-7
<
7
#5
-7
<
#6
-5 + 10
10
=
10 - 5
ASSIGNMENT
ODDS
P.20
ONLY
#19-31, 41-47, 53-55, 63