Which number produces a rational number when multiplied by 1 over 3

Any irrational number will remain irrational when multiplied by a rational number.

For example:

π * 1/3 = π/3

√2 * 1/3 = (√2) / 3

But if you multiply by a * rational * number, the result will stay rational.

Answer:

Any irrational number (e. g. π, √2, √3, etc.)