# Decimal Number System

Author: ARAS

The decimal number system is the standard system most commonly used in everyday life. The base (radix) is number 10 in the decimal system. Thus it has ten symbols (0 - 9)(0−9) which i.e, 0, 1, 2, 3, 4, 5, 6, 7, 8, 90,1,2,3,4,5,6,7,8,9.

The system number represents a number value in relation to its given base. A number has a single representation and different number systems have a different representation of the same number, based on its base value. In microprocessor programming systems, hex, octal, binary, and decimal number systems are used.

As one of the oldest number systems known, many ancient civilizations have used the decimal numeral system. The Hindu/Arabic numeral system has solved the challenge of expressing very large numbers in the decimal system. The Hindu-Arabic numeric system lists numerical locations in a number and operates using base power 10, and numerals are raised to the nth place.

For example, in the decimal system, take the number 1234.56:

• The number 4 is in position one (10^0)(100)
• The number 3 is in the position of tens (10^1)(101)
• The digit 2 is in the position of hundreds (10^2)(102)
• The number 1 is in the position of thousands (10^3)(103)
• The number 5 is in the tenths position because it comes after decimal point (1/10, \text{which is}  10^{-1})(1/10,which is 10−1) and 6 is in the hundredths (1/100), \text{which is}  10^{-2}1/100),which is 10−2) position
• So, the number 1234.561234.56 can also be stated as : (1 \times 10^3) + (2 \times 10^2) + (3 \times 10^1) + (4 \times 10^0) + (5 \times 10^{-1}) + (6 \times 10^{-2})(1× 103)+(2×102)+(3×101)+(4×100)+(5×10−1)+(6×10−2)