Calculating conductivity of a solution given molar conductivities and concentration
Just be explicit with all the units, including for the molar concentration, and be sure they cancel out properly.  You have $\pu{0.1 mol L-1}$ for the solution concentration, but your $K$ values are in $\pu{S cm2 mol-1}$.

So convert your molar concentration to cubic centimeters (there are $\pu{1e3 cm3}$ in one liter) and you get $\pu{1e-4 mol cm-3}$.

Then when you multiply both values and your units cancel nicely to give you

$$\pu{1e-4 mol cm-3} \times \pu{247.5 S cm2 mol-1} = \pu{2.475e-2 S cm-1}$$