Algebra II (Honors) Chapter 1 St. Augustine Preparatory School 2015/2016

Real Numbers What are real numbers? Any number that can be placed on a number line. Let’s take a look at -4, -2.5, the square root of 2, and pi.

Real numbers can be broken into categories Natural Numbers Whole Numbers Integers Rational Numbers and Irrational Numbers

Real numbers can be broken into categories Natural Numbers – you use these to count from 1, upwards. N = {1, 2, 3, 4,….) Whole Numbers – all of the natural numbers and zero W = {0, 1, 2, 3, 4….) Integers – all of the natural numbers, their opposites, and zero. I = {…-2, -1, 0, 1, 2…}

Real numbers can be broken into categories Rational Numbers: - All numbers that can be written as a quotient of integers (a/b, b cannot = 0) - Includes terminating decimals and repeating decimals - Examples: 1/8, 1/9, 1/3, 12/25

Real numbers can be broken into categories Irrational Numbers: - Have decimals that neither terminate or repeat - Examples: pi = 3.14159…. sqrt(2) = 1.4142135…. - These numbers cannot be written as quotients of integers

Classify the following numbers 12 i) pi -6.2 j) 9/4 -7 k) 4.565656 sqrt(4) l) 179 sqrt (5) m) 3.45x102 4/9

Number Lines Place the following on a number line (without a calculator): -5/2 , sqrt(2), 2.6666…, and 4.

Number Lines Number lines of inequalities: 2 < x ≤ 4 x > 4 or x < 2

Practice Questions Page 15 #24-34 Page 16 # 57-59