ratio
Dimensionlessexact by definition
A dimensionless quantity is a pure number, formed when two quantities of the same kind divide out and leave no unit behind. Efficiency, strain, Reynolds number, refractive index, coefficient of friction and safety factors are all of this kind. The conversion factor of one is exact by definition, since there is no physical unit involved.
Watch out: Dimensionless does not mean arbitrary. Most such numbers only mean anything alongside the definition that produced them: a Reynolds number depends on which characteristic length was used, a friction coefficient on whether it is static or kinetic, and an efficiency on what was counted as input. A pure number without its defining ratio is not information.
| 1 | 1 |
One ratio in every dimensionless unit
| 1,000,000,000,000 | part per trillion (ppt) | |
| 1,000,000,000 | part per billion (ppb) | |
| 1,000,000 | part per million (ppm) | |
| 100,000 | per cent mille (pcm) | |
| 10,000 | basis point (bp) | |
| 1,000 | per mille (per mille) | |
| 100 | percent (%) | |
| 1 | ratio (—)this unit |
Solvers that use dimensionless