The last four numbers ... -6, -3/2, 0, and 9 ... are rational numbers.
We can't be sure about 5.73773777..... . You haven't said whether it
goes on forever, or ends after 100 or 1,000 or a million decimal places.
If it ever ends, or if it repeats every 8 or 37 or 10,000 digits, then
this one is a rational number too.