A dyne is a unit of force in the centimeter-gram-second (CGS) system of units. It is defined as the force required to accelerate a mass of one gram by one centimeter per second squared. One dyne is equal to 10-5 newtons.
An erg is a unit of energy in the CGS system of units. It is defined as the work done by a force of one dyne acting over a distance of one centimeter. One erg is equal to 10-7 joules.
Therefore, 1 dyne is equal to 10-7 joules / 10-5 newtons = 10-2 newtons / 10-5 newtons = 10^-3 = 0.001 newtons.
Thus, 1 dyne is equal to 10^-3 joules, or 1 erg.