1. (as opposed to fake numbers?)
REAL NUMBERS
(as opposed to fake numbers?)

2. Two Kinds of Real Numbers
Rational Numbers
Irrational Numbers

3. Branching Real Numbers
Rational Irrational
Now let’s break these subsets down further!

4. Rational Numbers A rational number…
is a real number that can be written as a ratio (fraction) of two integers.
written in decimal form is terminating (ends) or repeating (same pattern of numbers).

5. Examples of Rational Numbers16
1/2
3.56 -8
1.3333…
- 3/4
Can you write 16 as a ratio?
Now try writing -8 as a ratio!

6. Natural Numbers
One of the subsets of rational numbers, integers and whole numbers
So what do natural numbers branch off of?

7. Natural Numbers All of your counting numbers
What numbers do you count with?

8. Whole Numbers One of the subsets of rational numbers and integers
So what do whole numbers branch off of?

9. Whole Numbers
All positive numbers that are counting numbers plus zero.
How can you remember that zero goes with whole numbers?
Examples: 0, 1, 2, 3, 4, 5 …

10. Integers One of the subsets of rational numbers
So what do integers branch off of?

11. Integers
Integers are rational numbers because they can be written as fraction with 1 as the denominator.
*Remember*
Rational numbers can be written as a ratio (or in other words, a fraction)

12. What are integers? Integers are the whole numbers and their opposites.
Examples of integers are 6
-12
186
-934
What do you notice about these integers?

13. Irrational Numbers An irrational number
is a number that cannot be written as a ratio (fraction) of two integers.
written as decimals are non-terminating (never end!) and non-repeating (no pattern).

14. Examples of Irrational Numbers
Square roots of non-perfect “squares” Pi 17
What is the square root of 17?
What is another non-perfect square?

15. Classify the following Numbers
What subset(s) do the following numbers belong to? Remember they could belong to more than one!
Whole, Integers, Rational, and Real

16. Classify the following Numbers (Con’t)4
Natural, Whole, Integer, Rational, Real -9
Integer, Rational, Real Π
Irrational, Real

17. Classify the following Numbers (Con’t)
3/4 or 0.75
Rational and Real 4
Natural, Whole, Integer, Rational, Real 15
Irrational, Real