Mathematics# Decimal system

## What is the decimal system?

## What is the decimal system for?

## Characteristics

## History

## Who invented the decimal system

## Decimal system symbols

## Examples

The decimal numbering system is also known as a **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 **arithmetic bases**, ten powers. The **Arabic** or Indo-Arabic **numbers** are the symbols used to represent the **decimal system** and it is composed of ten different digits: 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 **mathematical** aspects.

**Related Topics**

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

The decimal system is a **necessary** system in our daily lives. Most of the things we do are surrounded by **numbers** and it is necessary to have a way of **expressing** **them** in order to perform 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** 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**, because it helps us to **represent** things and large quantities, since numbers that are too large could not be easily represented.

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

From very ancient times, civilizations used different types of numbering systems to represent **numbers**. Some of them, like the **Roman** or the **sexagesimal** systems that were used in ancient **Babylon**, can still be observed today in our society, being the case, for example, when we use Roman numerals to represent centuries or years, or time, when we write it as 18:56. According to studies conducted by different **anthropologists**, the origin of this **system** is in hand **fingers**, which have been used for centuries to count. The development of numbers 1 to 9 originated in **India**, according to what was rescued from the **Inscriptions of Nana Ghat**, which date from the 3rd century BC. Sometime later, the **Arabs** began to use the numbers we know today.

This **numerical system** was created by **Hindu** peoples. Sometime after this system was created in **India**, the **astronomer**, mathematician and **geographer** **Al-Khwarizmi**, who was born in **Persia** in the year 780, introduced the **decimal numbering system** that is currently used all over the world. Al-Khwarizmi studied for a long time this system and the correct way to use it to make **calculations** with it. He perfected it with his own contributions and looked for a way to be able to use **zero** as a **number**. Thanks to his work, the system was translated into **Latin** and managed to be included in **Europe**, where it was decided to abandon the Roman numbering system and adopt the decimal numbering 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**.

The **symbols** used by 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 further to the **left** the number is, its number will be ten times more than it is worth. As such, in a natural number we can find the following figures:

- Units, the value it represents is worth,
- Tens, it’s worth 10 times its value,
- Hundreds, it’s worth 100 times its value,
- Thousand units, worth 1000 times its value,
- Tens of thousands, it’s worth 10000 times its value,
- Hundreds of thousands, worth 100,000 times its value,
- Units of a million, worth 1000000 times its value,
- Tens of a million, it’s worth 10,000,000 times its value,
- Hundreds of a million, it’s worth 100,000,000 times its value,

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

Written by Gabriela Briceño V.

Briceño V., Gabriela. (2019). *Decimal system*. Recovered on 28 October, 2023, de Euston96: https://www.euston96.com/en/decimal-system/