1. Opener/Warm Up #1 (8/25/10) Complete the following…show work
6 + 3 ∙ ½ + ¾
3. |-5| (-3)(2)
5. (2/3)( ¼ ) ÷(3+2)+(-2)(3)

2. Algebra 2 Numbers and Functions
The Complex Number System and Operations with Numbers

3. Repeating Decimals
Repeating decimals are decimals that contain a infinite number of digits.
Examples:
0.333… …
FYI…The line above the decimals indicate that number
repeats.

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

5. The Complex Number System
Real Numbers
Rational
Integers
Whole Numbers
Natural Numbers
Irrational
Imaginary Numbers

6. Imaginary Numbers
Imaginary numbers are all the numbers that deal with the square root of a negative number and contain the letter i in it

7. Real Numbers
Real numbers consist of all the rational and irrational numbers.
The real number system has many subsets:
Natural Numbers
Whole Numbers
Integers

8. 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.
Examples of irrational numbers: … …
(pi)

9. 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.

10. Integers Integers are the set of whole numbers and their opposites.
{…,-3, -2, -1, 0, 1, 2, 3,…}

11. Whole Numbers
Whole numbers are the set of numbers that include 0 plus the set of natural numbers.
{0, 1, 2, 3, 4, 5,…}

12. Natural Numbers Natural numbers are the set of counting numbers.
{1, 2, 3,…}

13. Venn Diagram of the Real Number System
Rational Numbers
Irrational Numbers

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

15. 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
Integers
Whole Numbers
6.36 …
Natural
Numbers -3
117

16. Solution -3 is an integer and a rational number.
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.
is an irrational number.

17. 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.

18. Properties of Real Numbers
Property Addition Multiplication Commutative a+b = b+a ab = ba Associative (a+b)+c = a+(b+c) (ab)c = a(bc) Identity a + 0 = a a•1 = a Inverse a + (-a) = 0 a(1/a) = 1
Distributive Property
a(b + c) = ab + ac

19. Examples of Properties
Name the property displayed:
-2 + (x – 5) = (-2 + x) – 5
2. (-2) ( -½ ) = 1
3. 2(4 – 5) = (4 – 5)2
4. x(y – w) = xy – xw

20. Order of Operations
Parenthesis/Grouping Symbols – Perform operations within the innermost grouping symbols according to Steps 2-4 below
Exponents/Powers – Perform operations indicated by exponents
Multiplication and/or Division – Perform multiplication and division in the order they occur left to right
Addition and/or Subtraction – Perform addition and subtraction in the order they occur left to right

21. Grouping Symbols
Grouping symbols include parenthesis, braces, brackets, numerators and denominators of fractions and underneath a radical or inside absolute value symbols.

22. Examples – Using Order of Operations
Evaluate the following:
22(12 + 8) 5
2. 52 ÷ (2 + 11)
3. 7 • ÷ 5