New (and not so new) scientists often don’t think about how many digits, or significant figures they should include when reporting numerical data. Unless you’re using a finely calibrated instrument, most readings aren’t accurate beyond one or two percent (about two significant figures). But that doesn’t stop a computer display or other electronic device from spitting out readings with a whole lot of digits. As a consequence, people commonly report data with much more precision than is justified by the measurement technique they use.

**Here’s the right way to report numerical data which has an error estimate** (e.g. an average +/- standard deviation, or an average +/- 95% confidence interval):

**1)** Report error estimates with only one sigificant figure, unless the first digit is a 1 or 2. In that case report two digits. Round up or down as appropriate.

**2)** Report the average result using as many significant figures as are justified by the digits in the reported error. Round as appropriate.

**Examples:**

Average = 43.695, standard deviation = 5.344, report 44 +/- 5

Average = 10.1113, standard deviation = 0.1249, report 10.11 +/- 0.12

Average = 23,765, standard deviation = 437, report 23,800 +/- 400

Average = 7,390,012, standard deviation = 251,912, report 7,390,000 +/- 250,000

Average = 0.00539, standard deviation = 0.00719, report 0.005 +/- 0.007

If your data has no error estimate and is a continuous number — say a ruler measurement — report only as many significant figures as can be accurately and reproducibly measured. If you can truly measure with an accuracy of 1/100th of an inch, report 17.35 inches, but if a reliable measurement can be made only to within 1/10th of an inch, report 17.4 inches.

In the case of a single discrete measurements (e.g. an accurate count of two-story houses in a town), it is correct to report the actual measurement with all digits: 13,271 houses. However, as soon as such measurements are averaged together and you have a variability estimate for the mean, follow the rules above. If the average over 12 communities = 13,271 houses, and the standard deviation = 598, report 13,300 +/- 600 houses (When randomly sampling a single town, this is your best guess of what the count of two story houses will be.).

Finally, when the accuracy of a measurement is unknown, use common sense to limit the number of significant figures to two, unless the first digit is a 1 or 2, in which case report 3 significant figures. [This implies a precision of approximately 1%; very few natural measurements are more precise than this when examined across multiple individuals, locations or time points]. For example, researchers may well have accurately counted 75,456 responding patients and 23,499 non-responders, but a more sensible way to report those numbers is 75,000 and 23,500. Similarly, 0.02987 would be reported as 0.0299 (three digits), and 0.0495 would be 0.050 (two digits).

**Exceptions: ** Sometimes using the same number of trailing or leading zeros is a useful technique to help facilitate comparisons. For example, using Table 1 on the left makes it easier to compare results up and down the column, even though some entries have more significant figures than are justified by the error measurement (Table 2 has the correct number of significant figures).

Table 1 Table 2

Avg. Error Avg. Error

0.0123 0.0007 0.0123 0.0007

1.2405 0.5674 1.2 0.6

0.0046 0.0030 0.005 0.003

0.0005 0.0004 0.0005 0.0004

And to make the comparison even easier, use a fixed width font!

Additional note on vocabulary: Precision is the extent to which repeated measurements agree with each other, accuracy is the extent to which the measurements match the true value.