What is the relationship between SI units and CGS unit of work?

Work SI unit = joule = N*m = [kg]*[m/s^2] * [m] = kg * m^2/s^2

Work cgs unit = erg = [g][cm/s^2][cm] = g*cm^2 / s^2

Then 1 kg * m^2 / s^2 * [1000 g/kg] * [100cm/m]^2 = 10,000,000 g*cm^2/s^2

The relation is 1 joule = 10,000,000 erg or 1 erg = 10^-7 joule