1. 1.3 Exploring Real Numbers

2. *All numbers are either Rational or Irrational*
Real Numbers:
The set of numbers containing both rational and irrational numbers
All the numbers we deal with are REAL 
*All numbers are either Rational or Irrational*
Rational Numbers:
Any number you can write as a fraction
Any decimal that either ends or repeats with a pattern
Irrational Numbers:
Any number that cannot be written as a fraction
Non-terminating, non-repeating wacky decimals
Examples?
If a number is irrational, it cannot belong to any other set
Vocabulary

3. If a number is rational, it could also be one of the following:
Natural Numbers:
1,2,3,4….
Also called Counting Numbers - These are the numbers we naturally count with
Whole Numbers:
0,1,2,3….
Only positive numbers and 0 (the word “whole” has an 0 in the middle!)
Integers:
Negatives and positive numbers and 0
No fractions or decimals
All the numbers you see on my number line
-2, -1, 0, 1, 2…
More Vocabulary…

4. 1. Identifying Sets of Numbers
a) -13
Rational numbers
Integers
b) 3.28 c)
d) 42
Natural numbers
Whole Numbers
1. Identifying Sets of Numbers

5. 2. Identifying Sets of Numbers
a) outdoor temperatures
Integers or Rational Numbers
b) the number of beans in a bag
Whole Numbers
Why not Natural Numbers?
2. Identifying Sets of Numbers

6. A counterexample is an example that proves a statement false.
True or False: All negative numbers are integers.
False
Counterexample?
3. Counterexamples

7. Inequality: compares the value of two quantities, using <, >, ≤, or ≥.
Compare the following fractions: /7
4. Inequalities

8. Write - , - , and - in order from least to greatest.
Find the decimal approximation of each.
- , - , -
5. Order fractions

9. 4. Opposites and Absolute Value
Opposites are on opposites sides of zero and are the same distance away from zero.
Examples?
-2 and 2, -6 and 6, etc.
Absolute Value is the distance a number is from zero.
a) l-2.5l
2.5
b) l7l 7
4. Opposites and Absolute Value

10. Wednesday, August 24 Keep your assignment out. We are going to grade.
Please bring a pen to class to use.
Remember, no stars, just a mark if the answer is wrong.
Wednesday, August 24

11. Answers for 1-18 Integers, rational Rational Irrational Answers vary
Natural, whole, integers, rational
Whole
Whole, integers, rational
Integers
Answers for 1-18

12. 20. False 22. True 24. > 26. > , 2.01, /6, -1/2, 2/ , 0.636, 7/ / /
Answers for even