Real numbers

Real numbers are all those numbers that are included within rational numbers. They can be positive, negative and include the number zero, as in the case of irrational numbers. These numbers can be written in different ways, some of them very simple, generally used in simple mathematical operations, and in more complex forms. Also included in this group of numbers are whole number fractions that have in their denominator numbers that are not null.

What are real numbers?

Real numbers are all those numbers found on the number line that make up the group of rational and irrational numbers, negative and positive, including the number zero.

Which are the real numbers?

The system of real numbers is formed mainly by two large groups, the rational numbers, which are all those numbers that can be expressed as the division of two whole numbers, and the system of irrational numbers whose decimal representation is expansive, infinite and aperiodic. Rational numbers can also be divided into subgroups, among which we can mention: non whole fractions with their negative notations; whole numbers including negative numbers and positive integers; the latter in turn include natural numbers and zero.

What are real numbers for?

Real numbers are digits that allow us to carry out all the mathematical operations necessary to solve a situation or problem. They also have as function, to designate the quantity of elements that have a certain group. They can be used to identify places or objects and to order and prioritize categories.


Among the main characteristics of real numbers we can mention the following:


They appeared as a need for the people of the primitive era to tell and solve problems that were constantly presented to them. It is recorded that the Babylonians used them to count, for example, their animals. The Egyptians used the fractions for the first time through mathematicians such as Pythagoras. During the 19th century, two important mathematicians, Georg Cantor and Richard Dedekind, made constructions and systemizations of real numbers. These two historical figures in Mathematics managed to systematize real numbers using a series of advances invented by them.


Real numbers are classified or divided into the following groups:

Real numbers properties

The property of the real numbers can change depending on the type of operation, being this the case, then we have the following ones:


The mathematical operations that can be performed using real numbers are: addition, multiplication, subtraction, division and potentiation or enhancement.


Written by Gabriela Briceño V.

How to cite this article?

Briceño V., Gabriela. (2019). Real numbers. Recovered on 7 October, 2021, de Euston96:

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