# Significant Figures when dealing with bearings

Significant figures are used to ensure that the value is precise, and fall in within error in the positive and negative direction.

327 degrees true can also be written as N33degreesW. As such, would this direction be 2 or 3 significant figures? It is understood that their total is 360 degrees, where addition and subtraction requires the lowest number of decimal points, not significant figures, but when using this in calculations, for example, with vectors, the question of the number of significant figures is apparent. It is important for rounding to minimise error.

This brings into the question whether the number of degrees in the 'hundred' place value actually is considered in precision, or is just an order of magnitude, as seen in p(O)H where the first value is an order of magnitude, not a significant figure.

• Dale is correct. In more detail, we never divide an angle measured in degrees by any other angle measured in degrees, other than the standard conversion factor $\frac{\pi\text{ radians}}{180^\circ}$. This means that significant figures does not make meaningful sense to degrees, and instead it is an additive quantity where decimal places is more meaningful to consider. Commented Feb 23 at 4:33

Whenever you are in doubt about significant figures, it helps to remember that significant figures are not used by professional scientists. Significant figures are used for students to have a very rudimentary approach to handling uncertainty while they learn some other scientific topic. When you reach an "edge case" with significant figures then you should use an actual uncertainty analysis instead. In that case you would explicitly write $$(327.0 \pm 0.5) \ ^\circ$$ where the term after the $$\pm$$ is the expanded standard uncertainty of the bearing.