Download Algebra 2 Honors Section 1.1 Handout Sets of Numbers

Algebra 2 Honors
Section 1.1 Handout
Sets of Numbers
Objectives


Produce examples of various sets of numbers
Classify numbers based on which sets they belong to
Notes
Complex, Real, and Imaginary Numbers





What is 𝑖?
Complex number: a number that can be written in the form 𝑎 + 𝑏𝑖, where a and b are real
numbers
Real number: a number that has a point on the number line
Imaginary number: square roots of negative numbers
How are these three sets of numbers related? Draw a figure below with examples:
Negative Numbers, Zero, and Positive Numbers

How are these sets of numbers related to real numbers? Draw a figure below with examples:
Rational Numbers vs. Irrational Numbers

A rational number is one that can be expressed as the ratio of two integers; an irrational number
cannot
Checkpoint 1:
2
15
̅
1.6
1. Classify these numbers as rational or irrational: , 4, 3. 3̅, √2, √
3
̅̅̅̅̅̅̅̅̅̅̅̅̅̅
, −6. 12459002
2. Develop a practical way to determine if a number is rational or irrational
Integers and Their Subsets





Integers are whole numbers and their opposites
Natural numbers are positive integers
Digits are 0, 1, …, 9
Even numbers are integers divisible by 2
Odd numbers are integers not divisible by 2
More on Irrational Numbers




Most irrational numbers you encounter are radicals
Are all radicals irrational?
Some irrational numbers such as 𝜋 or 𝑒 cannot be expressed as a radical of a rational number;
they are called transcendental numbers
What about 𝑒 2 , 𝑒 𝜋 , 𝑒 + 𝜋, or 𝑒 𝑖𝜋 ? Are they rational or irrational?