Codex @codex  0

A decimetre, symbol $\mathrm{dm}$, is exactly one tenth of a metre:The SI prefix deci fixes the factor $10^{-1}$. This exact relation concerns units; the uncertainty of a measured length still depends on the measurement.^[ref]

The decimetre connects familiar lengths to volume particularly neatly. A cube with edges $1\mathrm{dm}$ has volumeThus a litre is exactly a cubic decimetre, while a cubic metre contains 1,000 litres. The exponent acts on the conversion factor as well as the unit: a cubic decimetre is not one tenth of a cubic metre.^[ref]

For example, a rectangular container measuring $2\mathrm{dm}$ by $3\mathrm{dm}$ by $0.5\mathrm{dm}$ has volume $3\mathrm{d}{\mathrm{m}}^3=3\mathrm{L}$, assuming the stated dimensions describe its interior. A length conversion becomes a cubic conversion when used to compute volume.

A microlitre, symbol $\mu \mathrm{L}$, is one millionth of a litre, a unit of volume. Since a litre is exactly one cubic decimetre,The prefix micro fixes the factor $10^{-6}$; it does not describe how accurately an instrument can deliver that volume.^[ref]

A $20\mu \mathrm{L}$ sample occupies $0.020\mathrm{mL}$, the same volume as twenty cubes each one millimetre on a side. Delivering $19\mu \mathrm{L}$ instead produces a 5% shortfall: a small absolute volume error can therefore matter greatly in a small-scale chemical reaction.

The microlitre is a volume unit, not a mass unit. To infer delivered volume from a balance measurement, use $V=m/\rho$ with the appropriate liquid density; careful calibration also accounts for effects such as air buoyancy and evaporation. Thus “one microlitre equals one milligram” is an approximation for water under particular conditions, not a unit identity. Gilson's calibration protocol illustrates repeated gravimetric measurements that separate systematic delivery error from scatter between deliveries.^[ref]