The number "3.14159" by itself is rational, since it can be written as 314159/100000. However, the number pi (which is about 3.14159) is not rational, because it continues endlessly.
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Yes.
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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.