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 = $\frac{\kappa}{M}$. 

S.I. unit of :
$\kappa$ is $\pu{Sm}^{-1}$  &

$M$ is in $\mathrm{mol \, m^{-3}}$. 

Thus, Molar conductivity in S.I. is
$\mathrm{S \, m^2 \, mol^{-1}} \tag{1}$

When I substitute
1 m = 100 cm in (1).
I got new unit as 
$[\mathrm{S \, cm^2 \, mol^{-1}}] \times10^4$.
But in a book It was given as 

$[\mathrm{S \, cm^2 \, mol^{-1}}]  \times 10^3 \tag{2}$

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).