Final answer:
The maximum thickness of the metal plate is 1.02 inches, and the minimum thickness is -0.98 inches, although a negative thickness is not physically plausible and may imply a mistake in the question regarding the allowable error.
Step-by-step explanation:
The question concerns the allowable thickness variance for a metal plate in a mechanical device. To determine the maximum and minimum thickness of the metal plate, given an allowable error of ±1, we add and subtract the error from the nominal thickness.
Nominal thickness = 0.02 inch
Allowable error = ±1 inch
Maximum thickness = Nominal thickness + Allowable error = 0.02 + 1 = 1.02 inches
Minimum thickness = Nominal thickness - Allowable error = 0.02 - 1 = -0.98 inches
However, the answer with negative thickness doesn't make physical sense. In practical terms, a thickness cannot be negative, so there may be a misunderstanding or typo regarding the allowable error. If '1' stands for '1%', then the calculation would be quite different.