0 Is a rational number
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Yes, 0/3 is 0 which is a rational number
Zero (0) is a rational number, because it is a whole number and an integer.
No. 0 is a rational number and the product of 0 and any irrational number will be 0, a rational. Otherwise, though, the product will always be irrational.
The product of an irrational number and a rational number, both nonzero, is always irrational
It is the smallest non-negative rational number. Negative numbers are rational and are smaller.