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Question 1098821: Prove that 0.258 is irrational
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52852)   (Show Source):
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! .258 is not irrational.
it is rational, because it can be represented as a ratio between two whole numbers.
it is the decimal equivalent of the fraction 129/500.
here's some information about irrational numbers that you might find helpful.
https://www.mathsisfun.com/irrational-numbers.html
you should be able to prove that it is irrational by proving that it is not rational.
therefore try to prove that it is a rational number and you will find that it is.
if it is a rational number, then it can't be an irrational number.
it would be a proof by contradiction.
proving a number is irrational is extremely difficult.
here's a good reference that discusses the subject.
https://math.stackexchange.com/questions/62878/proving-irrationality
i used the method of contradiction in that i tried to prove it was rational.
if i succeeded, then it could not be irrational, because it was rational.
if i failed, that was not necessarily proof that it was irrational, as you can see from the reference when it took centuries to prove some numbers irrational.
since i succeeded, then it had to be rational, and consequently, not irrational.
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