Significant Figures Use by Laboratories

by | Apr 8, 2021 | Uncategorized

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What determines the amount of numbers you see on your report?

Each test that we do has a level of sensitivity associated with it.  Tests that you can do by visual inspection have the lowest sensitivity and are usually reported in whole numbers in a range of say 1 to 100 units or sometimes even higher.  But when you want to know how many things exist down into parts per million (ppm) or even parts per billion (ppb) we need to use “sensitive” analytical equipment. 

Let me give you an example of how “sensitive” relates to the very small amounts of pollutants/contaminants that may be in your sample.  Take one red marble and throw it into either a batch of 1,000,000 white marbles (ppm) or into 1,000,000,000 white marbles (ppb) and then try and find the red marble. It would be difficult, but since the marble is red it will stand out in a field of white – so we could use a less “sensitive” instrument to find the red marble in this scenario. 

Now if the marble was off-white instead of red it would be nearly impossible to find the off-white marble, so we would need to use a very “sensitive” instrument to separate and identify the off-white marble.  The numbers you see on your report have to realistically represent the sensitivity of what we are reporting to you.  This is where significant figure (numbers) come in, they let you know how numbers and zeroes are used in conjunction with decimal points to indicate “sensitivity.”

When a test is less sensitive we can’t really tell if every number is real so a result of 1243 mg/L might be pushing it if we had a reporting limit of 10 mg/L where the 3 is below what we could report for that test.  So for this test we might have assigned a 3 significant figures requirement, which would take your result and remove the uncertain 3 mg/L and now report 1240 mg/L.  If we wanted to be more confident in the number that we put on your report, we could assigned 2 significant figures to the test and we would report out 1200 mg/L. Notice how I removed numbers and replaced them with place holder zeros. 

When we are working with really small numbers like 0.1234 mg/L we don’t replace numbers with zero we just remove numbers from the far right.  For example if we were going to report to 2 significant figures we would report 0.12 (using basic rounding rules of course).  Better instrumentation allows us to go father right of the decimal point and less sensitive instruments force us towards the decimal point.  Here is a simple take on sensitivity, the more zeroes to the left of the decimal point indicates a less sensitive test; whereas, zeroes to the right of a number on the right side of the decimal point indicates a more sensitive test.

Knowing the sensitivity of our instruments we assign a number using significant figures on your report with confidence.

Significant figures have many more rules on how to determine which numbers are used.  The Libre Text website can be used to take your knowledge base to the next scientific level.

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