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Number (Higher) - Rational and Irrational Numbers
 
Rational Numbers | Irrational Numbers
 
Rational Numbers

A number that can be written exactly as a fraction is called a rational number.

For example, ¾, ½, 5.33333... , 6, are all rational numbers.

Note: 5.3333… = 5 1 (rational)  
    3    

If a decimal can be written down exactly, or is a recurring decimal, it is rational.

 

Irrational Numbers

A number such as square_root_2 is irrational because it cannot be written exactly as a fraction or decimal.

 pi_symbol  (pi) is irrational because it is a never ending, non-recurring decimal.

All square roots and cube roots that are not exact are irrational.

Example 1: Find an irrational number between 27 and 35.

 

(27 + square_root_2 ) is irrational.

Example 2: If we square an irrational number, we always get a rational number. Investigate:

  ( square_root_2)2 = 4 If we square a square root we get a rational number.  
    But ( pi_symbol)2 is still irrational.  
    So the statement is incorrect.