Background:

The Matter and anti-matter combine together in the warp core. In the warp core the antimatter and matter combine in the dilithium crystal, which is the only solid matter that does not react with anti-matter. The annihilation of the m/am creates a plasma that is directed towards the warp nacelles and interacts with the warp coils which creates a sub space distortion. When lots of these distortions are created it warps the space continuum and slips into sub space - faster than light.

Warp numbers do not directly refer to speed, but to power. Warp 1 is the power level required to enter the warp continuum, and is known as Threshold power. Warp 2 is twice that power level, etc.. Fractional warp is simply less than Threshold power while the ship, though traveling via warp field effect, is still "in" the Einstein space-time continuum at sub-light speed. The unit of power between whole warp factors for a given vessel is one "Impulse".