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Question 11974: I have a test tomorrow and i don't know the difference between rational and irrational numbers. Will you give me a detailed explanation on irrational numbers and rational numbers and give me some examples of each???
Thanks!!!
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! 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:
 ... 3.1415 blah blah blah....for ever
e = 2.712 blah blah blah
 = 1.414 blah blah blah
 = whatever it is
 = whatever
what about  ? why not that? well is 2, which is 3/6 or 8/4 or 400/200 etc...rational!
Does that help?
jon.
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