Any number with a finite amount of decimal digits - as well as periodically repeating decimals, such as 1/3 = 0.33333..., or 1/7 = 0.142857142857... - is rational.
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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.