1. Real Numbers: Number Systems
Objective: Classify numbers by their subsets and organize numbers on a number line.

2. Do Now:
What is a real number? Give me an example.

3. Real Numbers:
Real numbers are numbers that are not imaginary. These numbers can be grouped into two major classifications: rational and irrational.
Rational numbers: A real number that can be written as a ratio of two integers.
Irrational numbers: A real number that cannot be written as a ratio of two numbers.
Imaginary Numbers: A number that when squared gives a negative number.

4. Rational numbers include integers, whole numbers, and, natural numbers.

5. Natural Numbers {1,2,3,4,…} These are also known as counting numbers.
These are the numbers you use when counting.
No zero
No decimals
No fractions
No negative numbers

6. Whole Numbers
{0,1,2,3,…}
Whole numbers are like counting numbers but you start at 0.
No decimals
No fractions
No negative numbers

7. Integers
{…,-2,-1,0,1,2,…}
Integers are the counting numbers, zero, and the negative of the counting numbers.
No decimals
No fractions

8. The Real Number System Real Numbers Rational Numbers
Irrational Numbers 3
1/4 -2
15%
2/3
1.456
-0.8
10 2 7 2 3 5

9. Real Numbers
Rational Numbers
Irrational Numbers 3
1/4 -2
1.5
2/3
1.456
-0.8
10 2 7 2 3 5
Integers
Whole

10. Real Numbers Rational Numbers Irrational Numbers 3 1/4 -2 15% 2/3
1.456
-0.8
10 2 7 2 3 5
Integers
Whole
Like a Family Tree
Natural

11. Real Numbers
Notice there are still some more numbers to be classified.
Before we can go into rational and irrational numbers, let’s go over:
Absolute Values
Perfect Squares
Perfect Cubes
Radicals
Decimals
Fractions

12. Absolute Values: An absolute value is how far a number is from zero.
An absolute value is always positive.

13. Perfect Squares: A number created by squaring a whole number.
Let’s go through some perfect squares.
1^2 to 15^2

14. Perfect Cubes: A number created by cubing a whole number.
Let’s go through some perfect cubes.

15. Radicals: To take a square root of a number.
The inverse operation of squaring.
In order for a radical to exist in the real number system, the number under the square root or radical symbol, √ , must be positive.

16. Decimals:
A number that has a decimal point followed by digits that show a value smaller than one.
Types of Decimals:
Repeating
Non-repeating, Non-terminating
Terminating

17. Fractions A fraction is a part of a whole. Types of fractions:
Numerator: the top number that tells you how many parts you have.
Denominator: the bottom number that tells you how many parts the whole is divided by.
Types of fractions:
Proper fraction: numerator < denominator (i.e. ¼)
Improper fraction: numerator > denominator (i.e. 5/3)
Improper fractions can be written as mixed numbers (i.e. 3/2  1 ½)

18. Number Line:
All these different number classifications can be plotted on a number line.

19. Practice Place the sets on numbers on the number line. Set 1: 3 1/3
-0.6
11/4
√23
|5.7|
3.4
Set 2:
5/6
2.8 -5
|-5/4|
-3.453
-√8

20. Independent Work:
What are the two main categories real numbers are classified as?
Classify the following numbers. Then, place the following numbers on the number line below.
9/4, -2.7, √2, |-4.5|, 5

21. Exit Ticket
Based on what you have learned in class, what do you think are the key concepts from the lesson?