1-8 Number Systems Square Roots Add closure property? You will be allowed to use a calculator for tomorrow’s lesson but NOT on the CHAPTER 1 test! NO GRAPHING CALCULATORS! Algebra 1 Glencoe McGraw-Hill Linda Stamper

Natural or Counting Numbers REAL NUMBERS Rational Numbers: Any number that can be written in the form of . As a decimal they repeat or terminate. ex: Repeats ex: Terminates Irrational Numbers: ex:  and These must be represented by a symbol (ex: ), or as a rounded number, or in radical form because the decimal doesn’t repeat or terminate (stop). Integers: Whole numbers and their opposites (this means positive and negative whole numbers). ex: … ־ 4, 3, 2, 1, 0, 1 ־, 2 ־, 3 ־, 4 … Whole Numbers: Natural Numbers and zero. ex: 0,1,2,3… Natural or Counting Numbers ex: 1,2,3,4,…

You will need a calculator for today’s lesson You will need a calculator for today’s lesson. While you are allowed to use a calculator for today’s lesson, you will NOT be allowed to use one on the CHAPTER 1 test! NO GRAPHING CALCULATORS!

Keystrokes for TI-30X IIS You must learn how to use a calculator! There are many makes and models. Read the instruction booklet. Enter a problem into the calculator for which you already know the answer. For example: 2nd √ 4 = 2 4 √ = 2 Keystrokes for TI-30X IIS Keystrokes for TI-30X A

Keystrokes for TI-30X IIS Example 1 Evaluate the expression. Give the exact value, if possible. Otherwise, approximate to the nearest hundredth. You may use a calculator for this section. 2nd √ 8 = What is the positive square root of 8? Keystrokes for TI-30X IIS

Example 1 Evaluate the expression. Give the exact value, if possible Example 1 Evaluate the expression. Give the exact value, if possible. Otherwise, approximate to the nearest hundredth. You may use a calculator for this section. 8 √ = What is the positive square root of 8? Keystrokes for TI-30X A

Evaluate the expression. Give the exact value, if possible Evaluate the expression. Give the exact value, if possible. Otherwise, approximate to the nearest hundredth. You may use a calculator for this section. Example 2 What is the negative square root of 11? Example 3 What is the positive and negative square root of 1.69?

The inequality symbol points to the smaller value! To compare real numbers, find a decimal approximation for each number and then compare. The three dots are an ellipsis. In math, an ellipsis is used to indicate that the numbers continue in the same pattern. The inequality symbol points to the smaller value!

Replace each with <, >, or = to make a true statement. Example 4 Example 5 Example 6 Example 7

Order from least to greatest. Example 8 Example 9 Remember: To compare real numbers, find a decimal approximation for each number and then compare.

1-9 Coordinate Plane All coordinate plane graphs must be completed on grid paper.

A coordinate plane is formed by two real number lines that intersect at a right angle at the origin. The horizontal axis is the x-axis and the vertical axis is the y-axis. y II I The coordinate plane is divided into four regions called quadrants. • x III IV

Each point in a coordinate plane corresponds to an ordered pair of real numbers. (–2,3) • The first number identifies the x-coordinate and the second number identifies the y-coordinate. x y

• Graph the coordinate (3,4). The first number identifies the x-coordinate and the second number identifies the y-coordinate. x y

• Example 1 Graph the coordinate (4,–2). The first number identifies the x-coordinate and the second number identifies the y-coordinate. x • y

Example 2 Graph and label the coordinates in the same coordinate plane: A (3,–1), B (–4,0), C (–5,2), D (2,–4), E (0,3), F (0,0). E • C • B • • x F • A • D y

Example 3 In which quadrant or on which axis does each ordered pair lie? B. C. D. E. F. G. H. IV E • x-axis II IV y-axis origin III I H C • • B • F • x • A G • • D y

Coordinates are written as ordered pairs. You must use parentheses! Example 4 Write the coordinates of each point. D • A B C D E F G Coordinates are written as ordered pairs. You must use parentheses! (3,–2) G • (–4,0) (–5,–2) (2,4) (0,–3) (0,0) (–4,3) B • F • x C • • A • E y

Homework 1-A13 Pages 50-52 # 22–27,38-41,56-59,73-75. (Scientific calculators OK).