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The rational numbers are all numbers that can be expressed as a fraction, that is, as the quotient of two whole numbers. The word 'rational’Derives from the word‘reason', Which means proportion or quotient. Examples: 1, 50, 4.99.
In the mathematical operations that are done daily to solve everyday questions, almost all the numbers that are handled are rational, since the category It covers all whole numbers and a large part of those with decimals.
Both rational fractional numbers and irrational (its counterpart) are infinite categories. However, these behave differently: rational numbers are understandable and, insofar as they can be represented by fractions, their value can be approximated with a simply mathematical criterion, this is not the case with irrational numbers.
Examples of rational numbers
Rational numbers are listed here as an example. In the cases of these being numbers fractional, its expression is also indicated as a quotient:
- 142
- 3133
- 10
- 31
- 69,96 (1749/25)
- 625
- 7,2 (36/5)
- 3,333333 (3/10)
- 591
- 86,5 (173/2)
- 11
- 000.000
- 41
- 55,7272727 (613/11)
- 9
- 8,5 (17/2)
- 818
- 4,52 (113/25)
- 000
- 11,1 (111/10)
The most operations that are performed between rational numbers they necessarily result in another rational number: this does not happen, as we have seen, in all cases, as in the operation of the establishment and not of the empowerment.
Other typical properties of rational numbers are the equivalence and order relations (the possibility of making equalities and inequalities), as well as the existence of inverse and neutral numbers.
The three most important properties are:
- The associative
- The distributive
- The commutative
These are simply demonstrable from the condition inherent to all rational numbers of can be expressed as quotients of whole numbers.
Recurring numbers
A very particular category of rational numbers, which often gives rise to confusion, is that of periodic numbers: these are made up of infinite numbers but can be expressed as a fraction.
There are many recurring numbers. The simplest of them is the one that arises from dividing the unit into three equal parts, equivalent to 1/3 or 0.33 plus infinite decimal places: not because of its infinity condition, it becomes irrational.
Irrational numbers
The irrational numbers are those that fulfill the most recognized functions for the purposes of mathematics and geometry: undoubtedly the most important number in this science of ideal figures is the number pi (π), which expresses the length of the perimeter of a circle whose diameter (that is, the distance between two opposite points) is equal to 1.
The PI number is approximately 3.14159265359, and the prolongation can be extended to infinity to meet your definition of inability to express itself as a fraction.
The same happens with the length of the diagonal of a square taking each of the sides of that square as equal to unity: that number is the square root of 2, which is 1.41421356237. Both numbers, as the most important of the irrationals, have multiple functions derived from their primary role in geometry.
