SOLUTION: Prove that 0.258 is irrational

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Question 1098821: Prove that 0.258 is irrational
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52858)   (Show Source): You can put this solution on YOUR website!
.
In opposite,  0.258 =   is a rational number.



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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