As an example of rounding, you say that if a tensile fails at 23,999 psi, that it does not meet the criteria. However, the lab reports the cross section of the tensile typically to 3 significant digits. Such as .749" wide x .488" thick. So with that data, the maximum amount of significant digits you can have is 3. The cross sectional area is .365512, which rounds off to .366 sq in. The lab might also report the force requried to break the specimen as 8770 (8771.9 is required to get to 23,999lb) since thier machine is only accurate to the nearest 10 lb. So if you use .366 area, and 8770lb, your tensile comes in at 23,961 lb. Does that pass or fail? If the lab happened to report to 4 significant digits, they could have reported .7485" wide x .4875" thick and 8772 lb. In this case, the tensile comes in at 24040lb. Does this pass or fail? It was the same test, just different significant digits!!
You shouldn't be at the mercy of how the lab reports the data either. Your lab should follow standard industry practices based on how thier machines are calibrated. Your tensile data can only be as accurate as the least accurate measurement in the system. Standard rounding practices should be used since you don't actually know if the test was 23,999lb or not since measurements were not that accurate.