the real numbers and absolute value section 2.1. irrationalsrationals integers whole natural real...
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THE REAL NUMBERS AND ABSOLUTE VALUE
SECTION 2.1
IrrationalsRationals
Integers
Whole
Natural
2
3
.75
5
3
102 0
4
5.34
.14923...
8
1 25
Real Numbers
( _______ , ___________)
Irrational numbers – Decimal that never ________ and never ____________.
Real numbers – the set of both ____________ and _______________ numbers.
rational
irrational
endsrepeats
Rational numbers – Any number that can be written as a decimal that either ___________ or ___________________.ends repeats
Integers - ... 4, 3, 2, 1, 0,1, 2, 3, 4,...
( ___________ , _________, ___________)negatives zero positives
Whole numbers -
0,1, 2, 3, 4,...
( _______ , ____________)zero postives
Natural numbers -
1, 2, 3, 4,...
( _____________ )postives
negatives positiveszero
0 1 2 3 4-1-2-3-4
Symbols used for ordering numbers:
Less than
greater than
Equal to
Less than or equal to
greater than or equal to
Example 1: Insert an ordering symbol to make each statement true.
5 ____ 71 8______
2 16
4.8 ___ 4.7 24 ____ 63
Try these….
3 ___ 6 8.5 ___ 8.6
1 3___
2 537 ____ 97
A. B.
C. D.
On the number line, two numbers that lie on opposite sides of 0 and are the same _______________ from 0 are called ______________.
distanceopposites
8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8
The opposite of 6 is _____.
The opposite of -3 is _____.
-6
3
3 3
When finding the opposite of any number, use the opposite symbol.
6 opposite
6 6
opposite 3
The opposite of a positive is always __________.The opposite of a negative is always __________.The opposite of zero is always _______.
negativepositive
zero
Example 2: Evaluate each expression:
2
3
0
7.4 3.2
A.
B.
C.
2
3
0
4.2
Try these…
4
7
0
6.2 2.7
D.
E.
F.
4
7
0
3.5
x x
The ________________ of a real number is the distance it is from ________ on a number line.
means the absolute value of The symbol
absolute valuezero
Example 3: Simplify:
7 14.2 0 9 4 A. B. C. D.
7 14.2 0 13
13
13
7.3
8 3
Try these…
F.
G.
E. 13
7.3
5 5