Why is -0.45, 5/12, 0, 247 rational or an irrational number.

All are rational.

Any number you can write exactly and completely, or any repeating decimal is a rational number. Any number that can only be written exactly using a symbol, such as π or √2, is an irrational number. Something like √6.25 is rational, because it can be written exactly as 2.5, without the symbol.

The idea of "rational" means the number can be expressed as the ratio of two integers. Any integer can be expressed as the ratio of itself and 1.

All of your numbers can be expressed as the ratio of integers:

... -0.45 = -45/100 . . . . any terminating decimal can be expressed as a ratio of integers by making use of the place value multipliers

... 5/12 . . . . is the ratio of integers

... 0 = 0/1

... 247 = 247/1