is a real number, and it is not irrational, it is RATIOnal because it
is the RATIO of two integers, 1 and 2.   

 and  are irrational numbers because they cannot be
expressed as the ratio of two integers.

Notice that the first five letters of the word "rational" is "ratio".  And
that means "the ratio of two integers".

In fact integers themselves are rational.  For instance the integer 
is rational because it can be expressed as the ratio of two integers  or even as .

Repeating decimals are rational because they can be expressed as a ratio
of two integers.

.639639639639639.....

is a rational number because it doesn't have to be expressed as that decimal
that repeats forever, for it can be expressed instead as  as
you can see from the following long division:

      .639639639.......
111)71.000000000.......
    66 6
     4 40
     3 33
     1 070
       999
        710
        666
         440   
         333 
         1070
          999
           710
           666
            440

etc. etc. etc.  

However this decimal

.232332333233332333332...

although it has a pattern, it in irrational because it is impossible
to find to integers that it is the ratio as we could above with 
.639639639639639.....

 is often believed to be the rational number  but
22/7 is 3.142857142857142857....

and it keeps repeating that block of digits "142857" over and over

whereas the first digits of  are 3.1415926535898...
and it never repeats a block of digits.

So  is only close to . It isn't  at all.

 is rational but  is irrational.

Edwin