# Computer Science XI

## Decimal Number System

In our daily life, we use a system based on digits to represent numbers. The system that uses the decimal numbers or digit symbols 0 to 9 is called as the decimal number system. This system is said to have a base, or radix, of ten. Sequence of digit symbols are used to represent numbers greater than 9. When a number is written as a sequence of decimal digits, its value can be interpreted using the positional value of each digit in the number. The positional number system is a system of writing numbers where the value of a digit depends not only on the digit, but also on its placement within a number. In the positional number system, each decimal digit is weighted relative to its position in the number. This means that each digit in the number is multiplied by ten raised to a power corresponding to that digit’s position. Thus the value of the decimal sequence 948 is: 94810 = 9 x 102 + 4 x 101 + 8 x 100 Fractional values are represented in the same manner, but the exponents are negative for digits on the right side of the decimal point. Thus the value of the fractional decimal sequence 948.23 is: 948.2310 = 9 X 102 + 4 X 101 + 8 X 100 + 2 X 10-1 + 3X10-2 In general, for the decimal representation of X = {…. x2x1x0 . x-1x-2x-3 ……} the value of X is X= Sixi10i where i = …… 2, 1, 0, -1, -2, …… 