Question

Is 5.78778777 a rational or irrational number?..

Answer 1

That number is the ratio of 578,778,777 to 100,000,000 , so it's rational.

Here's a surprising factoid:

ANY number that you can completely write down on paper with digits...
and a decimal point or a fraction bar if you need them ... is rational.

If you can write it down ... without saying "repeating" or using symbols ...
it's rational.