Question 11974
any rational number is one that can be written as a fraction, like a/b, where a and b are integers...whole numbers.


So, the following are all rational:


2 --> 2/1 or 10/5 etc

-4.1 --> -41/10

0.000345 --> 345/1000000

even 0.121212121212.. (repeating forever) --> 4/33
NOTE: all repeating numbers are rational.


OK on rational numbers?


Right then, irrational numbers are, fairly obviously now, those numbers that cannot be written as a fraction a/b.


Irrational numbers are numbers that tend to go on for ever, never repeating themselves...remember, if they repeated, they could be written as a fraction, like 0.12121212121212... was.


Now, if a number never stops, how the hell can we write it down? As soon as we stop writing, it becomes rational.

Take an example to show this, consider a number 0.12332458214369804532.. etc. It goes on for ever, never repeating. How do i write it? Perhaps i write it as 0.12332? well, if i do that, then this IS rational. It is the fraction 12332/10000.


So how do we write irrational numbers? well, we give them names instead.


Examples are:

{{{pi}}}... 3.1415 blah blah blah....for ever
e = 2.712 blah blah blah
{{{sqrt(2)}}} = 1.414 blah blah blah
{{{sqrt(3)}}} = whatever it is
{{{sqrt(5)}}} = whatever


what about {{{sqrt(4)}}}? why not that? well {{{sqrt(4)}}} is 2, which is 3/6 or 8/4 or 400/200 etc...rational!


Does that help?


jon.