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A Relativistic speed is a speed which is a significant proportion of the speed of light. Therefore scientific analysis must take the consequences of special relativity into account. A relativistic particle is a subatomic particle moving at relativistic speed.
The boundary for when a particle becomes relativistic is impossible to define, but a particle can generally be said to be relativistic when Newtonian mechanics no longer provides an accurate description which, within a margin of error of 1%, is 10% of the speed of light for the speeds of the associated masses under consideration.