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 in (1).
I got new unit as 
[S$cm^2$/$mol$]×$10^4$.
But in a book It was given as 
[S$cm^2$/$mol$]×$10^3$  ........(2),
where they have taken S 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 given in (2).