The product of a non-zero rational number and an irrational number can always be written as

Multiplying an irrational number by a non-zero rational number still gives an irrational number. If the product were rational, dividing it by the non-zero rational factor would make the original number rational, which is impossible. An irrational number has a decimal expansion that neither terminates nor repeats, so the answer is “a non-repeating, non-terminating decimal.”

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