Tolerances are critical specifications in manufacturing that define the acceptable range of variation for a part's dimensions, shapes, or features. These are typically expressed as upper and lower limits, ensuring that parts fit together properly and perform as intended, even if slight deviations occur due to manufacturing processes. Tolerances can be applied to dimensions like length, diameter, or angles, as well as to geometric features like flatness, roundness, and parallelism. By specifying appropriate tolerances, manufacturers can optimize production efficiency, control costs, and maintain product quality. For example, a shaft and its mating hole might have specific tolerances to ensure a proper interference or clearance fit, facilitating smooth assembly and function.