Question

How do you know if a decimal is an irrational or rational number?

Answer 1

A decimal is rational if it:

either ends and doesn't go on forever; OR
it is a repeating decimal.
A decimal is irrational if it goes on forever and ever and never stops without repeating.

The number: 5.77777777 is rational because it goes on forever, REPEATING the same number (the digit 7).

It can also repeat a group of numbers, like the number: 8.789789789789789789

See how the "789" is REPEATING over and over again and never stops? That is a rational decimal!