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... 

1.1412... 
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.
An overview of the types of numbers that are used in math. Links to other pages explaining each type in depth. Explains also that some numbers are not numbers at all.
A rational number is one that can be represented as the ratio of two whole numbers.
Other number topics
Scalar numbers
Counting numbers
Numbers that have factors
Special values
(C) 2011 Copyright Math Open Reference. All rights reserved
