I often see the topic of this question as a source of heated contention for technicians, quality, and engineers…
KL
Recently, I am having some heated discussion about significant figures, and the internet is not much help in resolving the issue. I am told that if we have five of something, only one significant figure can be used. I know this is wrong, but I cannot support my argument, can you help?
note: Significant figures are the digits in a calculation which have certainty or meaning contributing to its accuracy. In order words, you should use the specified, or appropriate, amount of digits in order to keep the integrity of the number.
My Response
The only exception to significant figures is when we are multiplying or dividing the number by exact quantities. If a quantity is definite then it’s considered reliable; meaning that you have full confidence in your number. If we know, for example, we have exactly eight CD cases – we do not have to consider this number when determining the amount of significant figures to be used.
For example, I just stacked two identical diskettes on my desk and they measure 0.66cm using a pair of calipers. When divided by 2, the average thickness equals 0.33cm/diskette, not 0.3cm. The reason this result can be used is because we have confidence that there are exactly 2 diskettes. In this case we could use 2.000, 2.0000000, and so on for our calculations, so that the resulting average is based on the number of significant figures on the actual measurement, not on the number of diskettes.
Additional Thoughts
This does not mean that you have confidence that each of the diskettes in this example are exactly 0.33cm, but you do have confidence in the average thickness of those two diskettes.
Situations such as these are some of the reasons why we often recommend our customers put their management, engineering and technical staff through a refresher course in mathematics.
-Andy
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