Perhaps the most convenient thing to do, **before advancing in an explanation about unlimited non-recurrent decimal numbers,** is to briefly review some definitions that will allow us to understand this type of number in its just mathematical context.

## Fundamental definitions

In this sense, perhaps the best thing is to focus this theoretical revision on two specific notions: the first of them, the concept of irrational Numbers,** as these are closely related to the notion of unlimited non-periodic decimals. Likewise,** lights should be thrown on the very definition of Decimal Numbers, in order to become aware of the nature of this class of numbers, of which the limited non-periodicals are a type. Here is each of them:

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## Irrational numbers

In this way, we will begin by saying that irrational Numbers will be those numbers that -different from their contraries, rational Numbers- can never be annotated or expressed in the form of a fraction, **since they have an infinite decimal part,** which is specifically characterized by not counting in their numbers any series or period that is repeated.

## Decimal numbers

As for decimal Numbers, they have been defined by Mathematics as those numbers that will serve to express both rational and irrational Numbers, **and that will be composed of two parts:**

**The units:**first there will be the units, which will always be made up of an integer, which can be positive, negative or even zero. At the same time,**being part of the decimal system, each element within the units will have a positional value, being then from right to left the following elements:**units, tens, hundreds, thousandths, units of a thousand, tens of a thousand, hundreds of a thousand, etc.

**Incomplete units:**on the other hand, in the decimal numbers there will also be a second part, also known as the decimal part, which will be conformed by a smaller number of the unit, which will be located between zero and one. Likewise, the elements that make up incomplete units will have a positional value, counting from left to right. Among them, tenths, hundredths, thousandths, ten-thousandths, etc. can be distinguished.

These elements will be found within the Decimal Number united -and at the same time separated- by a comma, even though some mathematical schools also accept the use of the period. **However, regardless of which of the two signs is chosen, the entire part of the decimal number – that is, the units** – will always be annotated to the left of the comma, while incomplete units will be annotated after it.

## Unlimited non-periodic decimals

Once each of these definitions has been reviewed, it may be much easier to approach an explanation of the numbers called Non-periodic Unlimited Decimals, which will constitute a subtype of unlimited decimals, **that is, those with infinite incomplete units.**

In this way, it can be said that the unlimited non-periodic numbers will be those decimal numbers that, in addition to having incomplete units that extend to infinity, **in them there is no series of numbers that are repeated,** that is, that their decimals are infinite and without periods. This type of numbers are also called aperiodic.

## Examples of unlimited non-periodic decimals

However, it may be that the most efficient way to complete an explanation about unlimited non-periodic decimal numbers is through the exposition of a series of examples, where you can see in a practical way the structure that this type of decimal number has in its incomplete units, which are infinite and non-periodic. **Here are some of them:**

0,1298765438975…

3,981276543014…

25,1234765897154…

7,146527890614…

35,90765324915…

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