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Yes. Multiplying any number by zero results in zero.
It is zero. No matter how many times you multiply a zero, it is always zero. 0.
Smaller. The product of any positive number and a number between 0 and 1 will be smaller than the original number.
The rule is: "The product of zero and any number is zero." If the rule has a name, other than "The multiplication table of zero", I've never heard it.
The product of zero and any number is always 0.