Positional notation

Positional notation

Positional notation is a system in which each position has a value represented by a unique symbol or character. For each position, the resultant value of each position is the value of that character multiplied by a power of the base number for that numeral system. The position of each character or symbol (usually called a digit) counting from the right determines the power of the base that is to be multiplied by that digit.

For example, in the decimal or base 10 number system, each position starting from the right is a successive power of 10. The first position represents 10⁰, the second position 10¹, the third 10², the fourth 10³, and so on.

Fractional values are indicated by a separator, which varies by locale. Usually this separator is a period or full stop, or a comma. Digits to the right of it are multiplied by the base (10 in this example) raised to a negative power or exponent. The first position to the right of the separator indicates 10^-1, the second position 10^-2, and so on for each successive postion.

The total value of a number in a positional system is the total of each individual multiplication of a digit and its associated base multiplied by itself the number times represented by its position less 1.

As an example, the number 2674 in a base 10 number system is :

( 2 x 10³ ) + ( 6 x 10² ) + ( 7 x 10¹ ) + ( 4 x 10⁰ )

( 2 x 1000 ) + ( 6 x 100 ) + ( 7 x 10 ) + ( 4 x 1 )