Tell which measurement is more precise 178 in or 12 ft?

They are both as precise as the measuring tools. Precision is affected by the error introduced by the measurement or in a dimension, often known as the tolerance.

A measurement in inches has a greater resolution than one in feet. 12 times the resolution in fact. However, a measurement of 178 inches that can be up to 15% out is not as precise as a measurement of 12 feet with a 1% possible error.