Measure it with a micrometer, mark it with a chalk
line, then cut it with an axe. You probably experience some form of
this every day. It’s common to mix analytical instrumentation,
glassware, and reagents that have varying degrees of accuracy. Which
one of us hasn’t used a graduated cylinder in a colorimetric procedure
then reported a result with four significant digits? The colorimeter
may be that accurate, but the graduated cylinder has a much lower
level of accuracy. In the end, results are reported that are no where
near the accuracy implied by the written result. If you know how
significant the digits are in any measurement, then you may be able to
reduce your workload and produce more accurate and usable numbers in
your laboratory.

That is why understanding significant digits is crucial to producing
and reporting accurate results. A result of an analysis cannot be
reported using more significant digits than the number of significant
digits in the least accurate measurement used in the procedure. For
example, 75 mL of a sample (using a 100 mL graduated cylinder with an
accuracy to two significant digits) is diluted with water into a 500.0
mL volumetric flask (with an accuracy to four significant digits).
This solution is then reacted with a reagent and the resulting color
change is measured on a colorimeter (accurate to four digits). Since
the graduated cylinder is the least accurate link in this procedure at
two significant digits, the reported result should have only two
significant digits.

Determining significant digits is fairly easy to do:

Any nonzero integer is significant. For
example, 54.89 has four significant digits. 15 has two significant
digits.

Zeros may be significant depending on
where they are in the number.

Any zero between nonzero integers is
significant. 504 has three significant digits. 9008 has four
significant digits

Zeros to
the right of a nonzero integer may or may not be significant. 5000 may
have one, two, three, or four significant figures. With the available
information, it cannot be determined. However, zeros to the right of a
nonzero integer and after a decimal point are significant. 5.00
has three significant digits, 500.0 has four significant digits.

Finally, zeros to the left of a number are not significant. 0.005 has
one significant digit. 0.675 has three significant digits.

The next article will cover calculations using numbers
with different significant digits and how to round these numbers to
give a reportable result.

The information in this article is very general. As usual, check your
federal, state, and local regulations. You may have additional
regulations or requirements that you must meet.

If you have any questions,
suggestions, or comments, please contact LPC Chair Paul Fitzgibbons at
(401) 222-6780 ext 118 (__lab@narrabay.com__)
or Tim Loftus at (508) 949-3865 (__timloftus@email.msn.com__).
You can also visit our website at newea.org. Once on the website,
press the Lab Practices button.