13 mg MgSO4 $\Rightarrow$ 12 × 10^–3 gm of MgSO₄
MgSO₄ hardness = $\frac{12 \times {10}^{-3}\mathrm{g}}{{10}^3\mathrm{g}} \mathrm{x} {10}^6$= 12 ppm
$\Rightarrow$12 g of MgSO₄ in 10⁶ g of 

water hardness in terms of
${\mathrm{CaCO}}_3=12 \mathrm{x} \frac{100}{12}=10\mathrm{ppm}$