The hardness of water sample containing ${10}^{-3}M$  $MgS{O}_4$ expressed as $CaC{O}_3$ equivalents 
(in ppm) is _____________( Molar mass of $MgS{o}_4$ is 120.37 g / mol)

${10}^{-3}$molar $MgS{o}_4\equiv {10}^{-3}$moles of $MgS{o}_4$ present in 1 it solutions

${10}^{-3}MMgS{o}_4\equiv {10}^{-3}MCaC{o}_3$

${10}^{-3}MCaC{o}_3={10}^{-3}\times 100gmCaC{o}_3$in 1 it water.

Ppm (interms of  $CaC{o}_3$ )  $=\frac{{10}^{-3}\times 100}{1000}\times {10}^6$
$=100ppm.$