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

2. Real Numbers Real Numbers are every number.
Therefore, any number that you can find on the number line.
Real Numbers have two categories.

3. What does it Mean? The number line goes on forever.
Every point on the line is a REAL number.
There are no gaps on the number line.
Between the whole numbers and the fractions there are numbers that are decimals but they don’t terminate and are not recurring decimals. They go on forever.

4. Real Numbers REAL NUMBERS 154,769,852,354 1.333
-5, … -8 61 π
49%

5. REAL NUMBERS
NATURAL
Numbers
WHOLE
Numbers
IRRATIONAL
Numbers
INTEGERS
RATIONAL
Numbers

6. Two Kinds of Real Numbers
Rational Numbers
Irrational Numbers

7. Irrational Numbers
An irrational number is a number that cannot be written as a fraction of two integers.
Irrational numbers written as decimals are non-terminating and non-repeating.

8. Examples of Irrational Numbers
Pi ∏

9. Rational Numbers
A rational number is a real number that can be written as a fraction.
A rational number written in decimal form is terminating or repeating.

10. Examples of Rational Numbers16
1/2
3.56 -8
1.3333…
- 3/4

11. Try this! a) Irrational b) Irrational c) Rational d) Rational
e) Irrational

12. One of the subsets of rational numbers
Integers
One of the subsets of rational numbers

13. What are integers? Integers are the whole numbers and their opposites.
Examples of integers are 6
-12
186
-934

14. Integers are rational numbers because they can be written as fraction with 1 as the denominator.

15. Types of Integers
Natural Numbers(N): Natural Numbers are counting numbers from 1,2,3,4,5, N = {1,2,3,4,5, }
Whole Numbers (W): Whole numbers are natural numbers including zero. They are 0,1,2,3,4,5, W = {0,1,2,3,4,5, } W = 0 + N

16. REAL NUMBERS
NATURAL
Numbers
WHOLE
Numbers
IRRATIONAL
Numbers
INTEGERS
RATIONAL
Numbers

17. What categories of Real Numbers do these numbers belong in?

18. Comparing Rational and Irrational Numbers
When comparing different forms of rational and irrational numbers, convert the numbers to the same form.
Compare and
(convert -3 to …
… > 3 7 3 7

19. Practice

20. Ordering Rational and Irrational Numbers
To order rational and irrational numbers, convert all of the numbers to the same form.
You can also find the approximate locations of rational and irrational numbers on a number line.

21. Example Order these numbers from least to greatest.
¹/₄, 75%, .04, 10%, ⁹/₇
¹/₄ becomes 0.25
75% becomes 0.75
0.04 stays 0.04
10% becomes 0.10
⁹/₇ becomes …
Answer: , 10%, ¹/₄, 75%, ⁹/₇

22. Practice
Order these from least to greatest: