REAL Numbers

b

a

b

a

Rational #’s Irrational #’s

Whole #’s 0, 1, 2, 3 …

Integers: …-2, -1, 0, 1, 2 …

Rational #’s ( ) (1/2, 2/3, 5/1, 0.5, 0.666…, 5)

b

a e2

0.1010010001…

What is a set?

A collection of items (called “elements”)

0, 1, 2, …

“Set builder notation”

‘a’ and ‘b’ are integers, b ≠ 0b

a

Converting between fractions and decimals

?2

1 21

How can you tell from your calculator if the decimal “terminates”, “repeats”, or doesn’t terminate/repeat?

“rational numbers” (fractions) always either:1) terminate2) repeat

a > b: what can you say about:

a – b (positive/negative/zero?)a ≥ b: what can you say about:

a – b (positive/negative/zero?)a < b: what can you say about:

a – b (positive/negative/zero?)a ≤ b: what can you say about:

a – b (positive/negative/zero?)

Inteval notation(1, 2) Looks like the ordered pair: x = 1, y = 2

From the context where it is used you will be able to tell if it is an ordered pair or an interval of numbers.

(1, 2) “all of the #’s between (but not including) 1 and 2”

vs. inequality notation

(1, 2): means the same thing as: 1 < x < 2

[1, 2] “all of the #’s between (including) 1 and 2”

[1, 2]: means the same thing as: 1 ≤ x ≤ 2

Inteval notationvs. inequality notation

Convert to Inequality notation:

[1, 2)

(1, 2]

(∞, 2)

(∞, 2) U (7, ∞)

(∞, 2] U (5, ∞)

Graph

1 2

[ )

Your turn:

1.

2.

3.

4.

5.

8. (graph #4)

7. (graph #3)

6. (graph #2)

9. (graph #5)

Do you remember Properties of Exponents?

Power of a Power ?)( 32 x

Product of Powers ?))(( 32 xx

Power of a Product ?)( 2 xyNegative Exponent Property?2 x

Quotient of Powers ?2

5

x

x

Zero Exponent Property ?0 x