Perhaps it is best, prior to addressing each of the types of rational numbers conceived by Mathematics, is to briefly review the very definition of this type of number, so that we can understand this classification within its precise context.
In this way, it will begin by saying that Mathematics defines rational numbers as all those numbers, other than zero, that can be expressed in a quotient way. Consequently, this discipline states that rational numbers will consist of both whole numbers and fractional numbers.
On the other hand, rational numbers will be distinguished as those elements that constitute the q numeric set, which will have two subsets within it:
- First, within the Q set, the Integers will be found as a subset of this collection, then being defined as those elements used to represent exact quantities, and which are made up of positive integers, their negative opponents and zero.
- On the other hand, fractional numbers, which are understood as those non-integer or exact numbers representing a fraction or portion of the number, will also be found as a subset. These elements will be characterized above all by not being continuous – as are whole numbers – since between them there are infinite fractional numbers.
Types of rational numbers
With this definition in mind, it may be much easier to address each of the types of rational numbers, conceived by mathematics, and the main difference of which will lie in their decimal expression, as can be seen Then:
First, rational numbers, identified as exact decimal numbers, will be found, which will be characterized by numbers that have a certain number of decimal places. On the other hand, Mathematics also indicates that the exact decimals will always have a rest equal to zero. An example of such numbers will be as follows:
By reviewing this rational number, you will see how it meets the two characteristics of the exact Decimals, having limited or determined decimals, and also having a rest equal to zero.
Pure newspaper decimal
Within the different rational numbers, you will find those called pure periodic decimal numbers, which will be characterized by infinite decimals, which have figures that in addition to being equal are repeated again and again to the Infinite. Every time these decimals are repeated, Mathematics speaks of a period. An example of such rational numbers may be the following:
By reviewing this decimal, you will be able to see how it is repeated several times, so it can then be considered as a periodic Decimal. Likewise, the different sources point out that it should not always be annotated in this way, but that the period can be annotated as follows:
Equally, if this repeating period starts immediately after the comma that gives way to decimals, then this in addition to being considered periodic, it will be marked as a pure periodic decimal.
Decimal mixed newspaper
On the other hand, it can also happen that the decimal has a period – that is, a part that repeats indefinitely – that is not immediately presented to the comma that presents the decimal. In this sense, this decimal will be considered periodic, but mixed. An example of this type of decimal or rational number will be the following:
September 21, 2019