Significant Figures and Margin of Error—Or Why the Fourth Decimal Place in Your Potency Reading is Probably Meaningless: Page 2 of 2

May 15, 2020
Abstract / Synopsis: 

The concept of significant figures tells us, given the amount of error in a measurement, which numbers in a reading are meaningful and which are not. This is vitally important when determining whether low level values are real, for comparing readings over time, and for comparing results across laboratories and instruments. In a recent trend, cannabis laboratory customers are demanding more decimal places in the readings they are paying for, and third party laboratories have unfortunately obliged. I will show why those extra decimal places may be meaningless, and how to use significant figures to discern the true meaning of your cannabis analysis measurements.

A Practical Implication of Significant Figures

Growing hemp in the US was legalized with the passage of the 2018 Farm Bill (5). The bill states, in its current interpretation as promulgated by the United States Department of Agriculture (USDA) in its Interim Final Rule issued on October 29, 2019 (4), that legal hemp may not contain more than 0.3% by dry weight total THC. After the Farm Bill was passed there was great confusion about how to enforce that number. Some states read it literally and any value above 0.3000 was considered illegal. Other states took significant figures and margin of error into account and said that hemp up to 0.4% total THC was OK. This inconsistent enforcement is part of the hemp testing insanity I have written about in previous columns (6,7).

Here is the crux of the matter. If a hemp sample tests at 0.31% total THC, but the error is ±0.05%, this means that the true value of the reading is anywhere from 0.26% to 0.36%, straddling the 0.3% legal limit. Is this hemp crop legal or illegal? Is it fair to destroy a hemp farmer’s livelihood based on judgement of the accuracy in the hundredths decimal place?

Fortunately, the USDA’s Interim Final Rule has finally given us some guidance on this (4). The rule defines an “acceptable hemp THC level” which takes into account significant figures and margin of error. According to the rule (4), to calculate the acceptable hemp THC level as measured on a given instrument, take 0.3 wt.% total THC and add the margin of error to it. Thus, if the total THC margin of error on an instrument is ±0.05%, the acceptable hemp THC level as measured on that instrument is 0.35%. This means that any hemp sample reading from this instrument at or below 0.35% is legal, whereas any reading over this reading is illegal.

One of my complaints as to how the rule is written is that it rewards inaccurate readings. The rule did not establish any minimum acceptable margin of error. Thus, if faced with the choice of using an instrument with an accuracy of ±0.1% total THC versus ±0.05% total THC, one might be tempted to use the former because it gives a higher probability of passing your sample, particularly if it is a little hot.


I discussed the trend of cannabis laboratories reporting measured values to more and more decimal places. Significant figures determine how to report measured values taking into account the margin of error. We discussed how to properly compare and report values with the correct number of significant figures. This is important because cannabis businesses and regulators need the best quality data possible to make business and law enforcement decisions.

  1. B.C. Smith, Cannabis Science and Technology 1(3), 10–12 (2018).
  3. B.C. Smith, Cannabis Science and Technology 1(4), 12–16 (2018).
  5. 115th United States Congress, Senate Bill S.2667, Hemp Farming Act of 2018.
  6. B.C. Smith, Cannabis Science and Technology 2(5), 10–13 (2019).
  7. B.C. Smith, Cannabis Science and Technology 3(3), 12–15 (2020).

About the Columnist

Brian C. Smith, PhD, is Founder, CEO, and Chief Technical Officer of Big Sur Scientific. He is the inventor of the BSS series of patented mid-infrared based cannabis analyzers. Dr. Smith has done pioneering research and published numerous peer-reviewed papers on the application of mid-infrared spectroscopy to cannabis analysis, and sits on the editorial board of Cannabis Science and Technology. He has worked as a lab director for a cannabis extractor, as an analytical chemist for Waters Associates and PerkinElmer, and as an analytical instrument salesperson. He has more than 30 years of experience in chemical analysis and has written three books on the subject. Dr. Smith earned his PhD on physical chemistry from Dartmouth College.

How to Cite this Article

B.C. Smith, Cannabis Science and Technology 3(4), 10–12 (2020).