Yes.
If you mean 5.7777 as a terminating decimal it is 57777/10000
If you mean 5.7777... as a recurring decimal where the 7 repeats forever it is 57/9
If a decimal number terminates or repeats one or more digits forever it is a rational number.
Otherwise if a decimal number goes on forever but does not repeat any digits (eg √2 = 1.41421356...) then it is an irrational number.
yes
Yes.
yes
It must be a generalised rational number. Otherwise, if you select a rational number to multiply, then you will only prove it for that number.
Yes. Any rational number divided by another rational number is also rational.
-57777/10000
It is a rational number. It can be written as a fraction.
yes
Is 12.05 a rational number or irrational number?
1.96 is a rational number
It is a rational number, as it can be written as a fraction.
Yes, the sum is always rational.
There is no such thing as a number that is both rational and irrational. By definition, every number is either rational or irrational.
As much as, in these days of uncertainty, anything can be anything. As long as the constraints of a rational number are kept to, a rational number will always remain a rational number.
Yes, it is.
10.01 is a rational number
It is a rational number.