Decimal numbers

Perhaps the best thing, before going deeper into the definition of Decimal Numbers, it is advisable to review some concepts, which will understand a little more contextualized this type of numbers.


Fundamental definitions

In this sense, it may also be appropriate to delimit this theoretical revision to two specific notions: Integers and fractional numbers, because being aware of these concepts will help to understand how it is composed and what a decimal number represents. Next, each one of them:

Integers

In this way, we will begin by saying that integers have been defined by Mathematics as the elements that compose the numerical set Z, and that they are conformed in turn by natural numbers, their negative opposites and zero. Consequently, these numbers will serve to express whole quantities, absence of specific quantities, and even -thanks to the zero- the total absence of quantity.

Rational numbers

On the other hand, rational numbers are those elements that serve to represent the quotient existing between two integers, that is, the resolution of a fraction (mathematical expression used to account for fractional numbers, and that is composed of a numerator and a denominator, both different from zero). These numbers make up the Q set, a numerical group that is identified both as a subset of the Real Numbers (R) as well as the set in which Natural Numbers (N) and Integer Numbers (Z) can also be counted.

Decimal numbers

Once these definitions have been revised, it is certainly much simpler to approach an explanation of Decimal Numbers, which will then be understood as a form of representation of Rational Numbers, which will be composed of two classes of numbers:

  • Integer: first of all, you will find an integer, i.e. it can be positive, negative or even zero itself, but always pointing to an exact quantity.
  • Decimal number: this type of numbers, that is, decimal numbers, will also have a numeric part -called in the same- which will be composed of a non-exact part, and which will always be less than the unit, that is, it will be located somewhere on the Numeric Line between 0 and 1.

These two types of numbers, which will make up the decimal numbers will always be related, and at the same time separated by a comma, however in some mathematical traditions is also chosen to separate the elements of the decimal number with a period. However, whether it is a comma or a period, we will always choose to write the whole numbers to the left of this sign, while to the right we will do the same with the decimals.

However, it is likely that the best way to become aware of the shape of this type of numbers is through an example, which allows us to see in a practical way its structure, such as the one shown below:

Uses of decimal numbers

As for their use, Mathematics has pointed out that decimal numbers will have the mathematical task of expressing the quotient of rational numbers, whether they generate finite or periodic decimals, as well as irrational numbers, numerical elements that do not have the capacity to express themselves as a fraction, but constitute an infinite decimal, that is, a decimal number that has an entire part, but whose decimal part is infinite.

However, Decimal Numbers will also have their function in everyday life, serving to express the non-integer quantities of some elements. Therefore, one can find in the common language expressions such as “2.5 kilos of flour”; “3.75 liters of oil”; “7.5 centimeters wide”, etc. This type of numbers will be quite useful when looking for the precision of non-exact quantities, that is why they are widely used in recipes, instructions or technical or scientific texts, in which this accuracy of measurements is necessarily required.

Image: pixabay.com

Decimal numbers
Source: Education  
October 26, 2019


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