Rational NumberYou are currentlybrowsing as guest. Click here to log in 

A Rational Number is a number that can be expressed as a ratio. Examples:
Tricky.
The symbol for the rationals is usually Q so the above says $\sqrt2\not\in{Q}$
The set of Rational numbers is a countable set with size $\aleph_0$ . (see countable sets)
Euler's number (e) is an irrational number. You can see the proof that e is irrational.
A consideration of the mechanics of long division should convince that rational numbers must be represented by decimals expansions than 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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