The TI-30 calculator I purchased for $30 as a freshman engineering student took a 9-V battery and used eight bright red LEDs to display an answer. Often it rendered answers to simple division problems, for example, 22 divided by 7, using all eight digits—even though most of them contributed only to insignificant precision. Hence, the professors sternly warned us against the practice of “decimal point engineering.” They were simply trying to help us keep from falling into the trap of thinking all the digits in the answer shown on the calculator were meaningful.
That concept came rushing back as I listened to the animated discussion in a recent meeting of ASTM subcommittee C09.60, which deals with testing fresh concrete. The group met in Tampa, Fla., in December to consider, among other things, revisions proposed to ASTM C231-04, “Standard Test Method for Air Content of Freshly Mixed Concrete by the Pressure Method.” The discussion focused on the reporting requirements and the appropriateness of reporting test results to the nearest 0.1%.
The standard describes the two acceptable types of testing apparatus—both available from various manufacturers—as having “a means of direct reading of the air content.” Type A meters consist of having a graduated tube where the water level at a predetermined operating pressure indicates the percentage of air entrainment in the concrete. Type B meters use a pressure gauge that provides a direct reading of the percentage of entrained air. The test method specifically requires that the gauge must provide “for a range in air content of at least 8% readable to 0.1% ...” Both types of meters require periodic calibration, of course.
Given the two types of air entrainment testing apparatus, it's quite reasonable to have the test results reported to the nearest 0.1%. The rules of working with significant digits as applied to taking measurements allow for estimating the last digit between the two values, which are absolutely known. In other words, if the scale on a gauge is marked in tenths of a percent, one can report to the nearest hundredth of a percent. When the needle falls between 6.3 and 6.4, the technician estimates the final significant digit; for example, it might be 6.35.
Rounding—to get the reportable result to tenths of a percent—is covered by similar rules. If the last significant digit is less than 5, it is dropped. If it is more than 5, you add 1 to the last remaining digit. If it is exactly 5, you add 1 to the last remaining digit, but only if it is odd. So, in the case of the technician's reading of 6.35, the reportable reading would be 6.4%.
Now, here's the two-pronged problem that caused such a debate among those in attendance: First, Section 3.3 puts it bluntly, saying “the air content of hardened concrete may be either higher or lower than that determined by this test method.” It goes on to note several of the numerous factors that affect final in-place air content, including consolidation effort, uniformity and stability of the entrained air bubbles, pumping, and other factors. In short, the C231 test provides only a baseline measurement of air entrainment in freshly mixed concrete rather than any absolute value.
Secondly, and more important to those at the subcommittee meeting, was how the reported test result affects the acceptance of a load of concrete. Consider, for example, a specification that permits a maximum air entrainment of 6%. If the technician is required to report the result to the nearest 0.1%, the sample from above—with a reading of 6.35% reported as 6.4%—would be out of spec. However, the technician was instead required only to read to the nearest 0.1% and then report a value to the nearest full percentage, the same sample would have a reported air content of 6% and fall within spec. In either case, the test results themselves would have only been a pass/fail test with little connection to the long-term performance of the concrete once it was put in place.
Perhaps, there are two things to be learned from this debate. When using C231 testing as a basis for field acceptance, the limits should be sufficiently broad so that good concrete is not rejected. Also, when air entrainment test results come in at either extreme of acceptability, it should trigger some remedial action on behalf of the fresh concrete to better ensure its long-term performance and durability.