1. NUMBER
SYSTEMS ⅝ 25 √7 π
-4.15

2. 1, 2, 3, 4, … And so on, with NO end NATURAL NUMBERS
Natural numbers are the set of counting numbers.
1, 2, 3, 4, …
Natural numbers same as counting numbers. Ask participants what numbers we use are missing.
And so on, with NO end

3. 0, 1, 2, 3, 4,… And so on, with NO end WHOLE NUMBERS
Whole numbers are the set of numbers that include 0 plus the set of natural numbers.
0, 1, 2, 3, 4,…
What number was added? How would the addition of zero effect what we could do with our numbers?
And so on, with NO end

4. INTEGERS
Integers are the set of whole numbers and their opposites.
…-4,-3,-2 ,-1,0, 1, 2, 3, 4,…
And so on, with NO end, in Both directions
Give examples where negative numbers are used today. What numbers are still missing?

5. RATIONAL NUMBERS
Rational numbers are any numbers that can be expressed in the form of , where a and b are integers, and b ≠ 0.
They can always be expressed by using terminating decimals or repeating decimals.
Since rational numbers contain all the numbers we have talked about so far, are there any numbers that are not rational?
What makes them not “fit in”?
Examples:
⅔, 45, .29, ⅞, -106, √81, , 4.13

6. Terminating Decimals
Terminating decimals are decimals that contain a finite number of digits.
Examples:
36.8
0.125
4.5

7. IRRATIONAL NUMBERS
Irrational numbers are any numbers that cannot be expressed as .
They are expressed as non-terminating, non-repeating decimals; decimals that go on forever without repeating a pattern.
Give more examples.
Examples of irrational numbers: … …
π (pi) √2

8. All of these number systems fit together to form the Real Numbers.
Real numbers consist of all the rational and irrational numbers.
The real number system has many subsets:
Natural Numbers
Whole Numbers
Integers

9. Venn Diagram of the Real Number System
Rational Numbers
Irrational Numbers
Integers
Whole Numbers
Natural Numbers

10. Example
Classify all the following numbers as natural, whole, integer, rational, or irrational. List all that apply.
117 … -½
6.36 -3

11. To show how these number are classified, use the Venn diagram
To show how these number are classified, use the Venn diagram. Place the number where it belongs on the Venn diagram. …
Rational Numbers
Irrational Numbers
6.36
Integers π -3
Whole Numbers
Natural Numbers
117

12. Solution
Now that all the numbers are placed where they belong in the Venn diagram, you can classify each number:
117 is a natural number, a whole number, an integer, and a rational number.
is a rational number.
0 is a whole number, an integer, and a rational number.
… is an irrational number.
-3 is an integer and a rational number.
6.36 is a rational number.
π is an irrational number.

13. FYI…For Your Information
When taking the square root of any number that is not a perfect square, the resulting decimal will be non-terminating and non-repeating. Therefore, those numbers are always irrational.
Have participants give examples of square roots that are rational and square roots that are irrationall.