When a neuron fires is there such thing as partial firing?

No, a neuron either fires or it doesn't. Neurons do not partially fire. When a neuron fires, it is also known as an action potential. The action potential is a brief electrical impulse that travels along the neuron's axon. Action potentials are all-or-nothing, meaning that they either reach a certain threshold and travel down the axon, or they do not reach that threshold and do not fire.