Since pi is irrational, its product with any other number is also irrational.
The only exception is a multiple of its own reciprocal.
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No. If the rational number is not zero, then such a product is irrational.
You can add any irrational number.
Any irrational number, when multiplied by 0.5 will give an irrational number.
Any irrational number, added to 0.4 will give an irrational number.
Any irrational number will do.