The value of gravitation constant is $G=6.67\times {10}^{-11} \mathrm{N}·{\mathrm{m}}^2/{\mathrm{kg}}^2$ in SI units. Convert it into $CGS$ system of units.

The dimensional formula of G is $\left[{\mathrm{M}}^{-1}{ \mathrm{L}}^3{ \mathrm{T}}^{-2}\right]$. 

Using Eq. 

$n_1\left[{\mathrm{M}}_1^{-1}{ \mathrm{L}}_1^3{ \mathrm{T}}_1^{-2}\right]=n_2\left[{\mathrm{M}}_2^{-1}{ \mathrm{L}}_2^3{ \mathrm{T}}_2^{-2}\right]n_2=n_1{\left[\frac{{\mathrm{M}}_1}{{\mathrm{M}}_2}\right]}^{-1}{\left[\frac{{\mathrm{L}}_1}{{ \mathrm{L}}_2}\right]}^3{\left[\frac{{\mathrm{T}}_1}{{ \mathrm{T}}_2}\right]}^{-2}$

Here, $n_1=6.67\times {10}^{-11}{M}_1=1 \mathrm{kg},M_2=1 \mathrm{g}={10}^{-3} \mathrm{kg},L_1=1 \mathrm{m},L_2=1 \mathrm{cm}={10}^{-2} \mathrm{m},T_1=T_2=1 \mathrm{s}$

Substituting in the above equation, we get

$n_2=6.67\times {10}^{-11}{\left[\frac{1 \mathrm{kg}}{{10}^{-3} \mathrm{kg}}\right]}^{-1}{\left[\frac{1 \mathrm{m}}{{10}^{-2} \mathrm{m}}\right]}^3{\left[\frac{1 \mathrm{s}}{1 \mathrm{s}}\right]}^{-2}$

or, $n_2=6.67\times {10}^{-8}$

Thus value of G in CGS system of units is $6.67\times {10}^{-8}\text{ dyne }{\mathrm{cm}}^2/{\mathrm{g}}^2$.