Hardness of a water sample is 100 ppm ${\mathrm{CaCO}}_3$. Thus, molarity of ${\mathrm{CaCO}}_3$ is

Hard water has hardness = 100 ppm

Thus,${10}^6\mathrm{ml}\left({10}^3\mathrm{L}\right) \mathrm{water} \mathrm{has} =100 \mathrm{g} \mathrm{of} {\mathrm{CaCO}}_3=1 \mathrm{mole} \mathrm{of} {\mathrm{CaCO}}_3$

Thus, molarity $=\frac{\text{Moles}}{\text{Litre}}=\frac{1}{{10}^3}=1\times {10}^{-3}M$