Question

A mouthwash states it has among other ingredients, menthol 0.042% w/v. What is the correct interpretation?

This chemistry.stackexchange.com answer says it's weight per volume with unspecified units, so it is ambiguous. Kilograms per litre or grams per cubic light-year or whatever.
Alternatively, could it mean that 0.042% w/v is the concentration by weight and by volume, presumably because they are interchangeable?
The only reason to think they are interchangeable is that the density of menthol is 0.890 g·cm−3 which is close to water's density so perhaps it is also close to the density of this solution before the addition of menthol.
Percentage (one of hundred), ppm (one of million), ppb (one of billion) and similar units are relative quantities, relating two values of the quantity of the same kind. Like two masses/weights, two volumes, two molar amounts.

As this is source of possible misinterpretation, it is often marked explicitly like w/w, v/v, n/n. For these reasons, it is generally recommended to avoid these relative units, especially without explicit meaning, using explicit absolute quantities like e.g. mg/L,g/kg, μmol/mol,etc.
The mixed percentage (w/v) is a trick, assuming 1 mL of solution has mass ≈1 g and therefore 1 % w/v as 1 g in 100 g means also 1 g in 100 mL.
Particularly, 0.042 %w/v means 420 mg of the substance in 1 L of the product, as it is considered as 0.042 g in 100g(=100 mL).

Answer 1

The correct interpretation of 'menthol 0.042% w/v' is that there are 0.042 grams of menthol dissolved in every 100 milliliters of the mouthwash solution.

Step-by-step explanation:

The statement 'menthol 0.042% w/v' indicates the concentration of menthol in the mouthwash solution. This concentration is expressed as a mass-volume percentage, which means that there are 0.042 grams of menthol dissolved in every 100 milliliters of the mouthwash solution.

It is important to note that the units of solute (menthol) and solution (mouthwash) are the same, and the concentration is reported as a percentage. In this case, 0.042% w/v means 420 milligrams of menthol in 1 liter of the mouthwash product.