I know this might be a silly question but I am confused with different answers of internet. My question is:

Molar conductivity is given as:

Molar conductivity = $k÷M$.

SI unit of : k is S/m &

M is in mol/$m^3$.

Thus Molar conductivity in SI is S$m^2$/$mol$ ......(1)

When I substitute 1m=100cm I got [S$cm^2$/$mol$]×$10^4$ But in a book It was given as [S$cm^2$/$mol$]×$10^3$ ........(2) When S is taken in S/cm and molarity in mol/Litre. But where I was wrong.

If you feel the question too confusing just explain me How I can convert that SI unit given in (1) into unit (2).