Convert $1$ joule to ergs.

Joule : SI system, erg:CGS system

Work = Force x Distance = Mass x Acceleration x Length = Mass x $\frac{Length}{(Time{)}^2}\times Length$

Dimensions of work = $[W]=[M^1{L}^2{T}^{-2}]$

$\therefore a=1,b=2,c=-2.$

Now

SI system      CGS system

$M_1=1kg$      $M_2=1kg$

$L_1=1m$      $L_2=1cm$

$T_1=1s$      $T_2=1s$

Here $N_1=1,N_2=?$

$\therefore Using{N}_2=N_1{\left[\frac{M_1}{M_2}\right]}^a{\left[\frac{L_1}{L_2}\right]}^b{\left[\frac{T_1}{T_2}\right]}^c$

$=1{\left[\frac{1kg}{1g}\right]}^1{\left[\frac{1m}{1cm}\right]}^2{\left[\frac{1s}{1s}\right]}^{-2}$

$=1{\left[\frac{1000g}{1g}\right]}^1{\left[\frac{100cm}{1cm}\right]}^2$$=10^7$

$\therefore N_2=10^7$

So $1J=10^7$ erg