The decimal system is what mathematicians call a base-10 number system. This number system takes it name from the ten digits -- 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 -- required to represent the quantities in the system. A large number such as 4,534,896 when read represents four million, five-hundred thirty-four thousand, eight-hundred ninety-six. Yet, only seven digits are used to represent this large quantity in the base-10 system. Furthermore, as indicated, the position or place value of the number in the pattern indicates what the digit represents. For example, the four is seven places to the right of where the decimal point is understood to be, thus the four indicates a value equaling millions.
The binary number system came into use with the advent of computing. Today, digital technology makes extensive use of this basic number system, which can also be called a base-2 system. As the name indicates, the binary system uses only two digits, 0 and 1. The first fifteen numbers in the binary system are 1, 10, 11, 100, 101, 110, 111, 1000, 1001, 1010, 1111, 10000, 10001, 10010, 10011.
Another basic number system is made up of the natural numbers. Natural numbers are all whole numbers greater than zero. Numbers within the natural number system are what educators and mathematicians refer to as "the counting numbers," as this number system begins 1, 2, 3, 4, 5 and continues without end.
An integer is a whole number or zero. Integers can be either positive or negative. For example, -2 is an integer, as is 14. However, since integers include only whole numbers and zero, fractional numbers such as 4/5, or numbers with a decimal, such as 8.52, are excluded from this number system.
Rational numbers include the whole numbers, or a quotient -- the number that results from dividing one number by another -- of any whole numbers, excluding zero, used as a denominator. The system of real numbers includes all rational and irrational numbers, excluding any imaginary number. For example, a real number multiplied by the square root of minus one is an imaginary number, because there is no real number that can be used to represent the solution.