Guide
Exact and approximate numbers
Why the speed of light has no error bar and the mass of the Earth does, what it means for a constant to be defined rather than measured, and how to read a figure that has been rounded.
Three kinds of number wearing the same clothes
Written down, 299,792,458 and 8,848 and 86,000,000,000 look like the same sort of thing. They are not. The first is exact by definition, the second is a measurement that has been revised and will be again, and the third is a central estimate with a real spread on either side.
Nothing about the digits tells you which you are holding. That is why this catalogue records an exactness class alongside every quantity rather than leaving a reader to infer it from how round the number looks — roundness is a property of the units, not of the confidence.
Defined, measured, estimated
A defined value is exact because a standards body fixed it and then built the unit around it. The speed of light is not measured any more; it is 299,792,458 metres per second exactly, and the metre is whatever makes that true. The same happened to the kilogram in 2019, when the Planck constant was fixed and the physical cylinder in Paris was retired.
A measured value has an uncertainty even when nobody quotes one. Everest's height changed in 2020 not because the mountain moved appreciably but because the survey improved and the two countries either side of it agreed a joint figure.
An estimate is a central value standing for a range, and quoting it without the range is the most misleading thing you can do with a number. Eighty-six billion neurons is a good figure; it is also not a count, and no one has ever counted them.
Same shape, different kind
| Number | Kind | What that means |
|---|---|---|
| Speed of light, m/s | Defined | Fixed by definition since 1983. The metre is derived from it, so it cannot be measured more precisely. |
| Everest, metres | Measured | Revised to 8,848.86 m in 2020 by a joint Nepali and Chinese survey. |
| Neurons, billions | Estimated | A central figure from sampling, not a count, and quoted without a range far more often than it should be. |
The first can never change. The second changes when instruments improve. The third changes when the population does — and all three are written the same way.
Reading a rounded figure
When a figure is rounded, the rounding is a claim about how much of it is trustworthy. Quoting the Earth's mean radius as 6,371 km says the kilometre is meaningful and the metre is not; quoting it as 6,371.0 km would say something stronger and different.
This is why a change in the last digit of a large figure is usually not a disagreement. The catalogue treats two values as contradictory only when they disagree beyond the precision either of them claims — which is a different test from whether the digits match.
Numbers in this guide
Related topics
The defining constants and their fixed values are those of the International System of Units as revised in 2019.