1. THE REAL NUMBERS AND ABSOLUTE VALUE
SECTION 2.1

2. Real Numbers
Rationals
Irrationals
Integers
Whole
Natural

3. rational
Real numbers – the set of both ____________ and _______________ numbers.
irrational
ends
Irrational numbers – Decimal that never ________ and never ____________.
repeats
Rational numbers – Any number that can be written as a decimal that either ___________ or ___________________.
ends
repeats
Integers -
( ___________ , _________, ___________)
negatives
( _______ , ___________)
zero
positives
zero
postives
( _______ , ____________)
Whole numbers -
Natural numbers -
( _____________ )
postives

4. positives
negatives
zero -4 -3 -2 -1 1 2 3 4

5. Less than greater than Equal to Less than or equal to
Symbols used for ordering numbers:
Less than
Less than or equal to
greater than
greater than or equal to
Equal to

6. Example 1: Insert an ordering symbol to make each statement true.

7. Try these…. B. A. D. C.

8. On the number line, two numbers that lie on opposite sides of 0 and are the same _______________ from 0 are called ______________.
distance
opposites -6
The opposite of 6 is _____. 3
The opposite of -3 is _____.

9. The opposite of a positive is always __________.
When finding the opposite of any number, use the opposite symbol.
opposite
opposite
The opposite of a positive is always __________.
The opposite of a negative is always __________.
The opposite of zero is always _______.
negative
positive
zero

10. Example 2: Evaluate each expression:B. C.

11. Try these… D. E. F.

12. means the absolute value of
The ________________ of a real number is the distance it is from ________ on a number line.
absolute value
zero
The symbol
means the absolute value of
Example 3:
Simplify: B. C. A. D.

13. Try these… E. F. G.