The dimensional equation of force is $[F]=\left[M^{1} L^{1} T^{-2}\right]$

if $n_{1}, u_{1}$, and $n_{2}, u_{2}$ corresponds to $SI$ and $CGS$ units respectively, then $n_{2}=n_{1}\left[\frac{M_{1}}{M_{2}}\right]^{1}\left[\frac{L_{1}}{L_{2}}\right]^{1}\left[\frac{T_{1}}{T_{2}}\right]^{2}$$=1\left[\frac{k g}{g}\right]\left[\frac{m}{c m}\right]\left[\frac{s}{s}\right]^{-2}=1 \times 1000 \times 100 \times 1=10^{5}$

$\therefore 1$ newton $=10^{5}$ dyne.