# 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 (32 = 9), Also, a negative number squared is positive (-32 = -3*-3=9),
However, imagine numbers exist, say i, so i2 = −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? 