Barium sulphate is a very weakly soluble salt, and its molar solubility in water is 1.05 × 10⁻⁵…

Step 1. Grams per litre. $1.05 \times 10^{-5}\ \text{mol/L} \times 233\ \text{g/mol} = 2.45 \times 10^{-3}\ \text{g/L}$.

Step 2. Milligrams per litre. $2.45 \times 10^{-3}\ \text{g/L} = 2.45\ \text{mg/L}$.

Step 3. ppm. Taking $1\ \text{L} = 1\ \text{kg}$, this is $2.45\ \text{mg/kg}$, which is $2.45\ \text{ppm}$.