NUMBER SYSTEMS

(as opposed to fake numbers?) REAL NUMBERS (as opposed to fake numbers?)

Two Kinds of Real Numbers Rational Numbers Irrational Numbers

Branching Real Numbers Rational Irrational Now let’s break these subsets down further!

Rational Numbers A rational number… is a real number that can be written as a ratio (fraction) of two integers. written in decimal form it is either terminating (ends) or repeating (same pattern of numbers).

Examples of Rational Numbers 16 1/2 3.56 -8 1.3333… - 3/4 Can you write 16 as a ratio? Now try writing -8 as a ratio!

Irrational Numbers An irrational number is a number that cannot be written as a ratio (fraction) of two integers. written as decimals are non-terminating (never end!) and non-repeating (no pattern).

Examples of Irrational Numbers Pi Square roots of non-perfect “squares” What is the square root of 17? What is another non-perfect square?

Integers One of the subsets of rational numbers So what do integers branch off of?

Integers Integers are rational numbers because they can be written as fraction with 1 as the denominator. *Remember* Rational numbers can be written as a ratio (or in other words, a fraction)

What are integers? Integers are the whole numbers and their opposites. Examples of integers are 6 -12 186 -934 What do you notice about these integers?

Whole Numbers One of the subsets of rational numbers and integers So what do whole numbers branch off of?

Whole Numbers All positive numbers that are counting numbers plus zero. Examples: 0, 1, 2, 3, 4, 5 …

Natural Numbers One of the subsets of rational numbers, integers and whole numbers So what do natural numbers branch off of?

Natural Numbers All of your counting numbers What numbers do you count with?

Classify the following Numbers What subset(s) do the following numbers belong to? Remember they could belong to more than one! Whole, Integers, Rational, and Real

Classify the following Numbers (Con’t) 4 Natural, Whole, Integer, Rational, Real -9 Integer, Rational, Real Π Irrational, Real

Classify the following Numbers (Con’t) 3/4 or 0.75 Rational and Real Natural, Whole, Integer, Rational, Real Irrational, Real

Imaginary Number DEFINITION: Imaginary numbers are square roots of negative numbers.

IMPORTANT: They are all real numbers multiplied by i= (the square root of -1) EXAMPLE: 4i is an imaginary number and its square is -16.

Complex Numbers DEFINITION: A complex number is a number that can be written in the the form a+bi,a and b are real numbers and i is the imaginary unit. A complex number is a combination of a real number and an imaginary number.

EXAMPLE: (a+bi) + (c+di) = (a+c) + (b+d)I (3+2i)+(1+7i)=(4+9i)