thermodynamics - How should we express concentrations and partial pressures in ΔG=-RTlnK?

I understand that $K$ will be dimensionless. Let's say an equilibrium involving $K_p$ and the reaction is $\ce{A -> B}$, $K_p$ will be dimensionless. If the reaction $\ce{A + B -> C}$, then based on the formula of $K_p$ will be:

$$ \frac{(\text{partial pressure of C})}{[(\text{partial pressure B})\times(\text{partial pressure of A})]}$$

Since partial pressure can be in $\mathrm{Pa}$, or $\mathrm{bar/atm}$, with the difference between them will be roughly 100000 times. So the $K_p$s will have 100000 difference. Putting the $K_p$ into $\Delta G=-RT\ln K$, there will be a huge difference of $\Delta G$. So what units of $K_p$ should we use in this case?