Decimal system


The decimal numbering system is also known as the decimal system and consists of a positional numbering system . This positional system is a set of symbols and rules that allow us to form all the numbers that exist and that are valid. In the decimal system quantities can be represented using as arithmetic bases , powers of the number ten. Numbers Arabic or indo Arabic are the symbols used to represent the system decimaland is made up of ten different figures: zero (0), one (1), two (2), three (3), four (4), five (5), six (6), seven (7), eight ( 8), nine (9). This system is used worldwide and in all aspects of mathematics .


What is the decimal system?

The decimal system is a system of numbering composed of a series of symbols that respecting different rules are used to build the different valid numbers taking into account the base ten . It is the way to represent quantities using ten figures ranging from 0 to 9.

  • What is the decimal system for?
  • features
  • History
  • Who Invented the Decimal System
  • Decimal system symbols
  • Examples

What is the decimal system for?

The decimal system is a necessary system in our daily life. Most of the things we do are surrounded by numbers and it is necessary to have a way of expressing them to be able to carry out different activities, measure an object, perform different calculations, pay the bill in a store or restaurant. The decimal system allows us to construct all the numbers that are valid in the system. It is a way of counting the numbers. This system is a way that humanity has accepted to count. Another important function of this system is that it helps us to communicate by helping us to represent things and large quantities, since too large numbers we could not represent them so easily.



  • It is a decimal system because ten units of a certain order correspond to one unit of the higher order.
  • The decimal numbering system uses the number 10 as its base.
  • Because it is a positional system, the value of each number or digit will depend on its position within the numerical figure.
  • The sum of all the digits of the number multiplied by each power will give us the value of that number.


From very ancient times, civilizations used different types of numbering systems to represent numbers . Some of them, such as Roman or sexagesimal , systems that were used in ancient Babylon , can still be observed in our current society, being the case, for example, when we use Roman numerals to represent centuries or years, or the time, when we write it as 18:56. According to studies carried out by different anthropologists , the origin of the decimal system is in the fingersof the hands, which have been used for centuries to count. The development of the numbers 1 to 9 have originated in India , according to the rescue of the Inscriptions Nana Ghat , dating from the third century BC The Arabs , later, began to use the numbers we know to this day today.

Who Invented the Decimal System

This number system was created by the Hindu peoples . Some time after this system was created in India , the astronomer , mathematician and geographer Al-Khwarizmi , who was born in Persia in the year 780, made known the decimal numbering system that is currently used throughout the world. Al-Khwarizmi has long studied this system and the correct way to use it in order to do calculations with it. He refined it with his own contributions and looked for a way to use zero as a number . Thanks to his work, the system was translated into Latin and managed to be included in Europe , a place that decided to abandon the Roman numeral system and adopt the decimal numeral system. Today the system is used all over the world and, because it came to Europe through the Arabs and the works of Al-Khwarizmi, it is also known as the Arabic numbering system.

Decimal system symbols

The symbols used by the decimal system are the numbers from 0 to 9 and each of these numbers is associated with a certain value that depends on its position , the more to the left the number is towards the left side, its figure will be ten times what it’s worth. Thus, in a natural number we can find the following figures:

  • Units, it is worth the value it represents,
  • Tens, worth 10 times its value,
  • Hundreds, worth 100 times its value,
  • Units of a thousand, it is worth 1000 times its value,
  • Tens of thousands, worth 10,000 times its value,
  • Hundreds of a thousand, worth 100,000 times its value,
  • Million units, worth 1,000,000 times its value,
  • Tens of a million, worth 10,000,000 times its value,
  • Hundreds of a million, worth 100000000 times its value,


  • 539:  In this number the 3 occupies the place of the tens, therefore, its value is 30 (3 x 10). To understand it better, the number can be decomposed: 500 + 30 + 7
  • 329:  In this number the 3 occupies the hundreds place, therefore, its value is 300 (3 x 100). Therefore, the decomposed number will be: 300 + 20 + 9

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