How To Work Out Significant Figures

For anyone who hits the Significant Figures blog looking for an explanation of significant figures, you can find a quick cribsheet below or try out the significant figures calculator here.

Significant figures (sig figs or sf) are basically a way of expressing how accurately you measure something. It is a method of expressing error in measurement, in other words.

The most significant digit is the “first” digit of a number (the left-most digit). E.g. the most SF in the value 16.51 cm is that 1 in the “tens column, 6 is next, 0.5 , then 0.01. Thus, the least significant figure is the “last” digit of a number (the right-most digit). The further left you go in a number the more weight a value has, so that it’s more important to know that length is about 16 cm than to worry about the 0.01 cm (on most occasions).

So expressing 16.51 cm to two sig figs would be 17 cm, to three 16.5 cm and to four 16.51 cm.

The Significant Figures blog highlights the misuse of this system especially in the mainstream media. On the NASA site, one might see the average distance to the sun given as 149597870.691 km (1 astronomical unit, AU), for instance. This value is given to 12 significant figures, which is fine for NASA. But, most journalists would want a quick and easy number so it is usually rounded up to 150 million km (three sig digs). Problems arise, when those dudes next convert those modern km into the more traditional miles…and then give a value of 93.2 million miles, for instance.

This conversion somehow gains a sig fig in the conversion. BUT. SFs represent a measure of the error margins, the +/-, the give or take accuracy, so the conversion from km to miles has improved the accuracy of the value without actually physically determining this value with more precision. That’s just plain wrong. The only way to improve accuracy is to actually measure the distance more precisely (as NASA scientists have obviously done).

Anyway, I hope you get the point, check through the SF blog archives to find more examples of this kind of measurement nonsense.

Author: David Bradley

Freelance science journalist, author of Deceived Wisdom. Photographer and musician.