# Kinds of Numbers fact sheet

## Numbers include:

Natural numbers (whole numbers), integers, rationals, irrational, real numbers, imaginary, and complex numbers.

*Natural numbers*are counting numbers and whole numbers.

They are 1, 2, 3, 4, ... and sometimes include 0.*Integers*are positive and negative whole numbers.

Numbers that can be written without a fraction.

They are ... -4, -3, -2, -1, 0, 1, 2, 3, 4, ...*Rational numbers*are numbers that can be represented as a fraction and some decimal numbers.

(N/D) of two integers (is the a numerator and D is the denominator).

D is always defined as not zero (0).

If D is equal to one (1), then it is an integer.

Therefore, every integer is a rational number.

The set of all rational numbers is usually represented as**Q**.

A*decimal number*is a rational number if it terminates (has a finite number of digits) or repeats a finite sequence of digits (.125125 ...).

These statements hold true for any integer base number (binary, hexadecimal, ... ).*Irrational numbers*are numbers such as

√2 ≈ 1.41421356…,

π ≈ 3.14159265….

Numbers that do not terminate as a*decimal number.**Real numbers*include rational numbers (integers, fractions) and irrational numbers.

Real numbers can be represented as a point on a number line.

Where points represent equally spaced integers.*Imaginary numbers*are numbers when squared give a negative value. Usually when a positive number is squared, it gives a positive result (3^{2}= 9), Also, a negative number squared is positive (-3^{2}= -3*-3=9),

However, imagine numbers exist, say i, so i^{2}= −1.

Why? Because we need a number that can square to get -1 and we need a number whose square root of −1. Thus we imagine i to fit that need.*Complex numbers*are combinations of a real Number and an imaginary Number.

9 + i

9 + 3i

0.9 − 1.4i

−2 + πi

√2 + i/2

How are each represented on the number line below?