Final answer:
The greatest tread depth within any flight of stairs must not exceed the smallest by more than 3/8 of an inch to meet standard building codes for safety.
Step-by-step explanation:
The question pertains to the construction standards for stairways, specifically regarding the uniformity in the depth of treads within a single flight of stairs. According to building codes, the greatest tread depth variation allowed within any flight of stairs should not exceed 3/8 of an inch (0.375 inches). This means that the largest tread depth should be no more than 3/8 of an inch greater than the smallest tread depth to ensure safety and compliance with building regulations.