Oh, what a happy little question! Yes, 0.045 is a rational number because it can be expressed as a fraction where the numerator is 45 and the denominator is 100. Just remember, there are no mistakes in mathematics, only happy little accidents!
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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.