Oh, dude, 0.123333 is a rational number because it can be expressed as a fraction, like 12333/100000. Irrational Numbers are like those mysterious, never-ending decimals that never repeat, you know, like pi or the number of times I've procrastinated doing my laundry. So yeah, 0.123333 is just a chill rational number, no biggie.
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Well, darling, 0.123333 is a rational number because it can be expressed as a fraction, in this case, 123333/1000000. Irrational numbers are a whole different breed, honey, with non-repeating, non-terminating decimals like pi or the square root of 2. So, in this case, we're sticking with good old rationality.
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.