Math

# Examples of Irrational numbers

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.