Irrational numbers

An irrational number is a number that cannot be written in the form of a common fraction of two integers; this includes all real numbers that are not rational numbers.

When an irrational number is written in decimal form, it is written in the form of a non-terminating decimal that does not repeat. To show that the decimal doesn't end, it is typically written with the following symbol, "...", called an ellipsis.

Examples

The following are a few of the more commonly known irrational numbers:

π = 3.14159...
e = 2.71828...
= 1.41421...

No matter the number of decimal places we calculate these values to, there will always be another digit after it, hence the term non-terminating decimal.


Did you know??

There are more irrational numbers than there are rational numbers. Even though there are infinite of both types of numbers, we still know that there are more irrational numbers than rational ones. One way to think about this is that within even the relatively small set of natural numbers, the square root of all natural numbers that are not perfect squares (1, 4, 9, 16, etc), are irrational numbers. Having only listed the first 4 perfect squares, we've already reached the natural number 16. Between 1 and 16, there are 12 natural numbers the square root of which are irrational numbers. Furthermore, irrational numbers are non-terminating and non-repeating, so imagine adding many decimal places to each natural number along with all the combinations of digits we can use for each of the decimal places, and you can start to imagine just how many more irrational numbers there are!