In the mathematical field an Irrational Numbers are the Real Numbers that can’t be expressed in a fraction form. In a simple meaning an irrational numbers cannot be represented as a rational form. Irrational numbers are those real value numbers that can’t be represented as terminating or repeating Decimals. If we look at the history of famous irrational numbers, it is invented by the hippasus (a student) when he was trying to calculate the root of 2 as a fraction. In a more generic way irrational numbers means NOT rational. Rational numbers can be written as a Ratio of two integers. This can express by following example:
Here example 1:7.5 can be represented in the fractional form 15/2.
Example 2: 5 can be represented in the fractional form 5/1.
Example 3: 0.786 can be represented in the fractional form 786/1000.
The most famous example of irrational is ∏. Here value of ∏ =3.141592653. Now we can’t write down the value of ∏ into a fractional form whose values perfectly match to the actual ∏’s value. That’s why this value is known as irrational number.
Another most fabulous example of irrational number is √2. √2 value is 1.414213562.This is not perfectly match to any fractional numbers value. On behalf of irrational numbers value we can say that √2 is a irrational number.
The third most common example of irrational number is e. Here e stands for Euler’s number. Euler’s number is also calculated e for various types of decimal places without any pattern showing. Perhaps the numbers most easily proved to be an irrational are certain Logarithm.
It follows that
2m = 3n
The last but not least the epi is another example of irrational number. Chapernowne's number, 0.123456789101112131.this is constructed by concatenating the digits of the positive integers. At last for basic knowledge Point of view the above are the most popular irrational numbers, which cannot be expressed in the form of fractional number.