In SI system, the magnitude work done is joule. In another system, where the fundamental physical quantities are in gram, centimetre and second, the
magnitude of work is 

Joule is SI unit of work. The dimensions of work in SI.

$=\left[W_1\right]=\left[M_1{L}_1^2{T}_1^{-2}\right]$

But erg is CGS unit of work. The dimensions of work in

CGS unit $=\left[W_2\right]=\left[M_2{L}_2^2{T}_2^{-2}\right]$

As, $n_1\left(u_1\right)=n_2\left(u_2\right)$

or $n_1\left[M_1{L}_1^2{T}_1^{-2}\right]=n_2\left[M_2{L}_2^2{T}_2^{-2}\right]$

Here, $M_1=kg,L_1=m,T_1=s$

$M_2=g,L_2=cm,T_2=s$

$M_1=1000M_2,$

$L_1=100L_2$

$T_1=T_{2}andn=1$

$\therefore n_2=n_1\left[\frac{M_1}{M_2}\right]{\left[\frac{L_1}{L_2}\right]}^2{\left[\frac{T_1}{T_2}\right]}^{-2}$

$=1\left[\frac{1000M_2}{M_2}\right]{\left[\frac{100L_2}{L_2}\right]}^2{\left[\frac{T_1}{T_2}\right]}^2={10}^7$

$\therefore 1joule={10}^{7}erg$