Answer:
False
Explanation:
You want to know if it is true or false that "the number 0.3333... repeats forever; therefore it is irrational."
Rational
Any repeating decimal is a form of rational number. A number will only be irrational if it has an infinite number of decimal digits and never repeats.
The number 0.3333... is rational.
The offered statement is false.
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Additional comment
There are enough typos in your statement that we cannot be certain what the statement is. We can be certain that 0.3333... is rational.
Check to make sure the question being answered here is the one you want the answer for.