The decimal number system is the most commonly and widely used number system. We have ten elemental numbers in this number system. They are, respectively, 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. Since there are ten digits in this group, we say that the number system has a base or radix of 10. In the decimal number system, numbers greater than 9 are represented by repeatedly using these digits in a definite order. For example, let us consider the decimal number 123. This may be expressed in the form (123)10, where the subscript 10 represents the base or radix of number 123. It can be seen that 123 represents a short form of expressing numbers. This may be expanded as:
(123)10 = (1*102) + (2*101) + (3*100)
where digits 1, 2, and 3 are the coefficients of the appropriate powers of ten (i.e., 102, 101, and 100, respectively). Larger numbers can be expressed in similar fashion by writing them as coefficients of the powers of ten. In fact, in any number system, numbers are expressed as coefficients of appropriate powers of the radix of the system.