Examples of Irrational numbers

It is called irrational numbers to elements of the real line which are usually expressed by the ratio of two integers. These numbers cannot be written as a fraction .

The  irrational numbers within mathematics are those that can not be represented by fractional numbers ; In other words, they are those that have a decimal expression, infinite NOT periodic . Also, they can be defined as any real number that is not rational .

The first examples of irrational numbers can be seen here:

The fact that they cannot be expressed in the form of fractions, is because the decimal places continue indefinitely without repeating themselves .

Considering the set of Irrational numbers , it would be included in the real numbers, which are equivalent to all numbers with decimal , periodic and non-periodic expression .

Let’s build an example of  any irrational number like this:

2.90991999299993999994999999599999996 ………… ..

You can see that it is built by making the list of figures in the decimal tail infinite non-periodic .

Let us remember that the rational numbers are also part of the real numbers; but rational and irrational have no elements in common.

This is: I are included in  R ; Q is included in R   and;  IUQ = R with I ∩Q = Ǿ (it is empty)

More on Irrational Numbers: Properties

The origin of irrational numbers  took place in the Pythagorean School where, according to what is said, a student of Pythagoras named Hipaso discovered irrational numbers while working on a way to write the square root of 2 as a fraction and when he failed to do so, he put to this number the title of irrational .

In this school it was also called immeasurable numbers . Irrational numbers have certain properties that start from the aforementioned, from the fact that they are infinite non-periodic decimal numbers .

Thus we find that there are properties: commutative, associative , opposite element and; in the case of multiplications, these are distributive in relation to the operations addition and subtraction. Unlike the rational numbers, these irrational numbers do not have a neutral element and are NOT closed , let’s see examples:

  • -√2 + (- √2) = 0  and “0” is not irrational;
  • √2 x ( √2) = 2 and “2” is not irrational;

Also, the sum of a rational plus an irrational is an irrational and; the multiplication of an irrational by a rational is also irrational. Examples:

  • √3 + ( 2) = 2 + √3 an irrational
  • 2x ( √5) = 2 √5 is irrational

10 Examples of Irrational Numbers

  1. π (Pi) (3.141592653589…), one of the best known and most used. It has application to compare the diameter of a circle (D) with the length of the circle (L) . This is: L = π x D.
  2.  Euler number or e number (2.718281828459…)
  3. Golden Number (1.618033988749…).
  4. √2;
  5. √7 (2.6457513110645905905016157536393…)
  6. √99 (9.9498743710661995473447982100121 …);
  7. √122 (11.045361017187260774210913843344 …);
  8. √999 (31.606961258558216545204213985699…)
  9. E: it is the Euler number and it is the curve that is observed in electronic tissues.
  10. Golden: this type of number is known as the golden ratio and is used to express in irrational numbers the proportion between the two parts of a line.
  11. 2: 41421356328.
  12. 201: 177
  13. 19: 3588989.

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