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A numeral system is how we represent a number. The value of a number depends on the digit we use and its position.

For example, in decimal system (the most widely used system), we use ten figures for representing a number (0,1,….,8,9) and 89 has not the same value as 98, despite the fact that we use the same figures for representing both numbers.

Ideally, a numeral system will:

- Represent all the numbers (rational, integers, etc.)
- Use just one representation for each number.
- Reflect the algebraic and arithmetic structure of the numbers.

Source:

Some ancient numeral systems:

picture source

http://math.tutorvista.com/number-system.html

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