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Zero is a rational number. Rational numbers are numbers that can be represented by the division of two integers. Zero is zero divided by anything besides zero, so zero is rational.
In general, all whole numbers - numbers without digits after the decimal point - are rational. Some numbers with digits after the decimal point are rational as well, but not all of them.
0 Is a rational number
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.
The product of an irrational number and a rational number, both nonzero, is always irrational
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.