**Solution:**

Since gm/cc and Kg/m^{3} are CGS and SI units of density respectively. The dimensional formula of density is d = [ML^{-3}T^{0}] and comparing it with [M^{x}L^{y}T^{z}] we get,

x = 1, y = -3 and z = 0

n M L T |
n M L T |

We have, the unit conversion formula using the dimensional method is

\(n_2=n_1\left[\frac{M_1}{M_2}\right]^x\left[\frac{L_1}{L_2}\right]^y\left[\frac{T_1}{T_2}\right]^z\)

\(=19.3\left[\frac{1gm}{1kg}\right]^1\left[\frac{1cm}{1m}\right]^{-3}\left[\frac{1sec}{1sec}\right]^0\)

\(=19.3\left[\frac{1gm}{1000gm}\right]^1\left[\frac{1cm}{100cm}\right]^{-3}1\)

\(=19.3\times10^{-3}\times10^6\times1\)

= 19300

i.e. 19.3 gm/cc = 19300 kg/m^{3}