We are taught from a young age that two plus two equals four; it is a given just as the earth is round, despite recent controversy. But two plus two may not equal four due to two concepts: significant figures and rounding. But why should you care about either of those two concepts? If you are subject to permit limits or standards those concepts can be the difference between compliance and noncompliance.
The stringency of a limit depends on the significant figures used in the numerical representation. Say, for example, you have a limit of two parts per million (ppm). If the limit is expressed numerically with one significant figure it would be 2, while it would be 2.0 if expressed with two significant figures. At first glance those numbers appear to be the same, but in reality they are very different. The trailing zero after the decimal point is considered significant for a reason and impacts rounding conventions.
If your limit is expressed numerically as 2, you would be in compliance with any measurement less than 2.5 ppm as those values would round down to 2. If instead your limit was expressed as 2.0, the measurement would have to be less than 2.05. That extra significant figure (.0) is very important when it comes to how stringent a limit is and demonstrating compliance.
So the next time you are negotiating permit conditions or comparing limits, be sure to take note of the number of significant figures and any policy the permitting agency may have for addressing significant figures in compliance determination.
And for extra credit, the National Oceanic and Atmospheric Administration says, “While the Earth appears to be round when viewed from the vantage point of space, it is actually closer to an ellipsoid.”