Rational NumberYou are currentlynot logged in Click here to log in 

A Rational Number is a number that can be expressed as a ratio.

The rational numbers aren't all there is.
It surprised Pythagoras to discover that some numbers cannot be written as a ratio. For example, Root Two is irrational. In fact, between any two rationals there are infinitely many irrationals, and between any two irrationals there are infinitely many rationals. The problem is that Cantor showed that there are more irrational numbers than rational numbers.
Tricky.
The symbol for the rationals is usually $\mathbb{Q}$ so the above says $\sqrt{2}\not\in{\mathbb{Q}}$
The set of Rational numbers is a countable set with size $\aleph_0.$ (see countable sets)
See the page on Irrational Numbers for more information.
This next section deserves a page on its own, but finding a good name for it is hard ...
A consideration of the mechanics of long division should convince that rational numbers must be represented by decimals expansions that either terminate or repeat.
The converse is also true: decimal expansions that terminate or repeat can be expressed as a fraction.
For example:  let p = 0.143272727272727... (statement 1) 
Multiply by 100 two zeros, because the repeat is of length 2  100p = 14.3272727272727... (statement 2) 
Subtract, taking (2)  (1)  99p = 14.184 
Three decimal places, so multiply by 1000  99000p = 14184 
Divide both sides by 99000  so $p=\frac{14184}{99000}$ 
Consequently, irrational numbers must have infinite and nonrepeating decimal expansions and vice versa.
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