At what speed do the relativistic formulas for length differ from classical values by 1.00 %? (this is a reasonable way to estimate when to do relativistic calculations rather than classical.)

I believe you must have come across Lorentz factor. The Lorentz factor or Lorentz word is the factor by which period, distance, and relativistic mass alteration for an object whereas that object is moving. This is 1/sqrt (1-v^2/c^2). This computes the deviation from the classical values. One percent deviation means 1/sqrt (1-v^2/c^2) = 1.01