Yes because it can be expressed as a fraction in the form of 1/3
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no - 0.333333 is 333333/1000000, which is the ratio of two integers, the denominator not being zero, and that meets the definition of a rational number. Also, 0.333333, with the 3's repeating forever is 1/3, also a rational number.
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.