n the field of mathematics, the **decimal system** is a method of positioning the numbers. It was developed by Indian mathematicians . Later, the Arabs introduced it to Europe , where it received the name of Arabic numeral system.

## Summary

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- 1 Function
- 2 Decimal system in the Spanish language
- 3 Fractions
- 4 Search for prime numbers
- 5 Negadecimal system
- 1 Indications

- 6 Sources
- 7 References

## Function

It is a positional numbering system in which the quantities are represented using the number ten as a base, so it 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) and nine (9). This set of symbols is called Arabic numerals .

Except in certain cultures, it is the position system commonly used throughout the world and in all areas that require a numbering system. However, there are certain techniques, such as in computing, where numbering systems adapted to the working method are used, such as binary or hexadecimal . There may also be vestiges of the use of other numbering systems in some languages, such as quinary , duodecimal and vigesimal . For example, when counting items by the dozen , or when special words are used to designate certain numbers; in French , for example, the number 80 is expressed «*quatre-vingt* ”,“ four scores ”, in Spanish.

According to anthropologists , the origin of the decimal system is in the ten fingers that we humans have in our hands, which have always served as a basis for counting.

The decimal system is a positional numbering system, so the value of the digit depends on its position within the number.

So:

347 = (3 × 100) + (4 × 10) + (7 × 1).

347 = (3 × 10 ^{2} ) + (4 × 10 ^{1} ) + (7 × 10 ^{0} ).

Decimal numbers can be represented on the real line .

## Decimal system in the Spanish language

For the decimal separator, the Royal Spanish Academy advises to separate the integer part of the decimal, the comma should be used, as established by international regulations: The value of π is 3.1416. However, Anglo-Saxon use of the dot is also supported, widespread in some American countries.

For their part, the Language Academies recommend the point on page 666 of the Spelling: “In order to promote a process towards unification, the use of the point as a separator sign of decimals is recommended.” 2

In the past, a high comma (‘) was used as a separator.

- With that system, the number π would be written 3’14159.

As a thousands separator, the most usual thing in Spanish is to use a point , a subscript 1 as a separator of millions, a subscript 2 as a separator of billions, 3 of trillions, etc.

However, the RAE recommends separation by spaces so that there is no confusion with the decimals, grouping them every three digits (except for 4-digit numbers):

When writing numbers with more than four digits, these will be grouped three by three, starting from the right, and separating the groups by blank spaces: 8 327 451 (and not by periods or commas, as, depending on the areas, up to now: 8,327,451; 8,327,451). Four-digit numbers are written without spaces: 2458 (No. 2,458). In no case should the numbers that make up a number be distributed on different lines; for example: 12 345

678.

## Fractions

Some very simple fractions, like 1/3, have infinite decimal places . For this reason, some have proposed the adoption of the duodecimal system , in which 1/3 has a simpler representation.

- 1/2 = 0.5
- 1/3 = 0.3333 …
- 1/4 = 0.25
- 1/5 = 0.2
- 1/6 = 0.1666 …
- 1/7 = 0.142857142857 …
- 1/8 = 0.125
- 1/9 = 0.1111 …

## Finding Prime Numbers

In base 10, a prime number can only end in 1, 3, 7, or 9.

The remaining 7 possibilities always generate compound numbers:

- The finishes in 0, 2, 4, 6 and 8 are multiples of 2,
- Finishes 5 and 0 are multiples of 5.

## Negadecimal system

In this case, the base of the system is the negative number -10. Examples are presented:

- Write -1 on a negadecimal basis. -1 = -10 + 9 = 1 (-10) + 9 = (19)
_{-10} - Put 10 in the negadecimal base. 10 = (-1) (- 10) = (9-10) (- 10) = 9 (-10) + (- 10)
^{2}= (- 10)^{2}+1 (-10)^{1}+0 (-10 )_{0}= (190)_{-10 }^{[1]}

### Indications

- The usable figures are: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
- Orders:
*denials*(-10)^{0};*negadecenes*(-10)^{1};*negacentenas*(-10)^{2};*negamillares*(-10)^{3}, so on.