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YES!!! 2.78778777 is an irrational number because it has endless numbers, and a irrational number cant be put as a fraction but rational numbers can be put as a fractio!!
If by the ellipses you mean to say that the number 7 repeats forever after that point, then it is not irrational. Any number which can be expressed with repeating decimals is not irrational. For example, pi is an irrational number because it has no repeating decimals, but 0.33333333... is not irrational because it can be expressed by simply saying 0.3 repeated.
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