In the Western world, the decimal number system is the most widely used and familiar system for representing numbers. While there are other number systems in existence, the decimal system has become the default choice in society. The reason behind this can be attributed to the fact that humans have two hands (and two feet) with five fingers on each, making counting from 1 to 10 a natural process. Once you reach 10, you start over to reach 20, and so on. This is likely why the decimal system, which utilizes base 10 and ten different digits from 0 to 9, has gained such prominence.

Originating from India and popularized by Arabs, the decimal number system is also known as the Hindu–Arabic number system. The term “base 10” is used because it is characterized by its use of ten digits. However, what sets the decimal system apart is its positional nature. In this system, each digit holds a different weight or value depending on its position within a number. For example, the digit ‘1’ in the number ‘10’ has a different value than in the number ‘31’ because its position is different. This positional attribute is not present in all number systems.

An alternative example is the roman number system, which was widely used in Europe during ancient Rome and the late Middle Ages. Like the decimal system, it was also base 10. However, the roman system did not have positional digits. Instead, specific letters represented particular values. For instance, ‘X’ represented 10, ‘C’ represented 100, and ‘M’ represented 1000. In roman numerals, the decimal number 243 can be represented as ‘CCXLIII’.

In the decimal number system, any number can be broken down into the sum of other numbers, each multiplied by a power of 10 based on its position. The positions start at 0 from the right. For instance, 10^0 equals 1, 10^1 equals 10, 10^2 equals 100, and so on.

In this system:

  • The number 5 can be represented as 5 * 10^0
  • The number 42 can be represented as 4 * 10^1 + 2 * 10^0
  • The number 254 can be represented as 2 * 10^2 + 5 * 10^1 + 4 * 10^0

The decimal number system’s ability to decompose numbers based on positional values is a fundamental concept that underlies various mathematical operations and calculations.