Significant figures

Number of decimals?

Number of decimals?

Sometimes you see the advice to round up figures and present them with the same number of decimals. However, this is not a good advice because it does not take into account that figures need to be presented with a varying number of decimals to reflect the underlying precision of the figures. Using the same number of decimals will present some figures less precise than they are while others are presented as being more precise than they are. We have two types of figures to consider in a research project; raw data and calculated data.

Significant figures when presenting raw data

If an observation is exact such as number of participants or number of children in a family then the exact number should be given. However, a lot of retained raw data are measurements producing a figure that is not exact. It is an estimate. Example can be height, weight, cholesterol levels in blood etc. Figures that are estimates should be given with a precision that reflects the accuracy of the measurement. Raw data can be presented with many significant figures if you are measuring using a method with very high accuracy. However, you should present the raw data with few significant figures if your method of measuring / estimating is unreliable . This is elegantly explained in the (rather funny) video “Why are Significant Figures Important?” by Tyler DeWitt:

Significant figures when presenting calculated data

Significant figures are also of interest as soon as you present any type of descriptive statistics or inferential statistics. How do I know what number of significant figures are appropriate? The number of significant figures that should be used when presenting research results (such as mean, standard deviation, odds ratios, p-values, etc) is given by the size of the sample you have. As a rule of thumb the appropriate number of significant figures can be obtained by by taking the base 10 logarithm of the sample size and rounding to the nearest integer. The base 10 logarithm for a sample size of 100 is 2, for 1,000 is 3, for 10,000 is 4, for 100,000 is 5 and so forth.

Please note that if your raw data are very unreliable and only valid with one significant figure (unusual) it means that your calculated output should also be presented with only one significant figure. Please also note that a lot of significant figures will make your manuscript more difficult to read and in most situations there is no need to present more than 3 significant figures even if your sample size is large enough to allow more significant figures. Some examples of proper rounding of figures:

Result of a calculation / analysisTwo significant figuresThree significant figures
14.863351514.9
0.06534420.0650.0653
148.6772150149
0.00000214632.1 x 10-62.15 x 10-6

More about proper rounding of figures

Further details about how to round figures is explained in the video “How to Count and Round Significant Figures” by MahanChem:

You should cite this article if you use its information in other circumstances. An example of citing this article is:
Ronny Gunnarsson. Significant figures [in Science Network TV]. Available at: http://science-network.tv/significant-figures/. Accessed July 28, 2017.

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