Download Real Numbers & Absolute Value

THE REAL NUMBERS AND ABSOLUTE VALUE
SECTION 2.1
Real Numbers
Rationals
2
3
5.34
Irrationals
3
Integers
5
8
.75
102

0
Whole
.14923...
Natural
1
25
4
rational
Real numbers – the set of both ____________
and
_______________
numbers.
irrational
ends
Irrational numbers – Decimal that never ________
repeats
and never ____________.
Rational numbers – Any number that can be written as a decimal
ends
repeats
that either ___________
or ___________________.
Integers - ...  4, 3, 2, 1, 0, 1, 2, 3, 4,...
4,...
( ___________
negatives
, _________,
( _______
zero ___________)
, ___________)
positives
Whole numbers -
Natural numbers -
1, 2, 3,
zero
postives
(
_______
,
____________)
4,...
postives
( _____________
)
negatives
-4
-3
-2
positives
zero
-1
0
1
2
3
4
Symbols used for ordering numbers:



Less than

Less than or equal to

greater than or
equal to
greater than
Equal to
Example 1: Insert an ordering symbol to make
each statement true.

5 ____  7

4.8 ___  4.7

1
8
______
2
16

2
4 ____ 6
3
Try these….

A. 3 ___ 6

1
3
C. 2 ___ 5

B. 8.5 ___  8.6
D.

3
7 ____ 9
7
On the number line, two numbers that lie on opposite
distance
sides of 0 and are the same _______________
from 0
opposites
are called ______________.


8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8
-6
The opposite of 6 is _____.
3
The opposite of -3 is _____.
When finding the opposite of any number, use the opposite symbol.

6

3
3

opposite

  6
opposite

 3
negative
The opposite of a positive is always __________.
The opposite of a negative is always __________.
positive
The opposite of zero is always _______.
zero
Example 2: Evaluate each expression:
 2
A.     
 3
B.
  0 
C. 
2
3
0
 7.4  3.2 
4.2
Try these…
4
7
D.
 4
  
 7
E.
  0 
F.
  6.2  2.7  
0
3.5
absolute value
The ________________
of a real number is the distance
zero
it is from ________
on a number line.
The symbol
x
means the absolute value of
x
Example 3:
Simplify:
A. 7
7
B.
14.2
14.2
C.
0
D.  9  4
0
 13
13
Try these…
E.
13  13
F.
7.3 
G.
7.3
 8  3   5  5