What is a base for real number?
The base of a number is the size of the groups in a counting
system. The system we use is base 10. The smallest two-digit
number, 10, represents a group of ten units or 101. 100 is ten
groups of ten units or 102. 1000 is ten groups of ten groups of ten
units or 103, and so on. The base is also the number of different
digits used in the counting system including 0.
Computer designers and low level programmers are also familiar
with base 2 (binary), base 8 (octal) and base 16 (hexadecimal). In
binary, 10 represents a set of two units or 21, 100 is two sets of
two or 22, 1000 is two sets of two sets of two or 23, and so
on.
When a base other than 10 is being used, the base is often
written as a subscript after the number. For example, 101012 = 258
= 2110.