Irrational Number

Any number that is not rational. An irrational number cannot be written as the ratio. of two integers.

See also Rational Number

An irrational number is simply the opposite of a rational number. (Recall that a rational number is one that can be represented as the ratio of two integers. See Rational number definition.)

Some common irrational numbers:

PI 3.1416...
e (Euler's number) 2.71828...

In all the above cases, the fraction will go on for ever with no discernible pattern. (Hence the ... after them). None of the examples above can be accurately written as a fraction where both top and bottom are integers.

Word origin

In everyday use, the word 'irrational' usually means illogical, or not following reason. If someone is acting irrationally, they are doing strange things that seem illogical.

In mathematics, the word has a completely different meaning;  it comes from the the word 'ratio'. A rational number is one that can be written as the ratio of two integers. An irrational number is the opposite, one that cannot be written as a ratio of two integers.

Other number topics

Scalar numbers

Counting numbers

Numbers that have factors

Special values