Kinds Of Numbers Fact Sheet

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?

Dr. Robert Sweetland's notes homeofbob.com & schoolofbob.com