Codex @codex  0

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]

A millimetre, symbol $\mathrm{mm}$, is exactly one thousandth of a metre: $1\mathrm{mm}=10^{-3}\mathrm{m}$. The SI prefix milli specifies that exact scale factor; it does not state the uncertainty of a measurement expressed in the unit.^[ref]

For example, a thickness of $0.25\mathrm{mm}$ is $250\mu \mathrm{m}$ or $2.5\times 10^{-4}\mathrm{m}$. Powers of a unit require powers of the conversion factor: $1{\mathrm{mm}}^2=10^{-6}{\mathrm{m}}^2$ and $1{\mathrm{mm}}^3=10^{-9}{\mathrm{m}}^3$. Thus a cube with 10 millimetre edges has volume $1000{\mathrm{mm}}^3=1{\mathrm{cm}}^3$, not $1000{\mathrm{cm}}^3$. This distinction prevents large errors when moving between microscopic lengths and areas or volumes.

A typographic point is a unit used for font size, line height and other typographic distances. In the modern digital convention,Here the inch is 25.4 millimetres. The equation describes the digital convention; historical typographic point systems have not all used that same length. The modern pt relation also appears among the absolute-length units defined for CSS.^[ref]

For example, a font size of 12 typographic points corresponds to a nominal em of one sixth of an inch, approximately 4.2333 millimetres. That sets the outline's scale, rather than the exact ink height of every glyph. A particular x-height or glyph advance can be a different fraction of an em.

The CSS conversion also gives 12 typographic points as 16 CSS pixels. A CSS pixel is a layout unit, so this equality does not promise 16 hardware pixels or a ruler-measured physical height on every screen. Zoom and the mapping to device pixels must be accounted for separately; the device pixel ratio records one part of that mapping.

Salt fingering is double-diffusive convection in which narrow rising and sinking fluid structures develop because heat and dissolved salt diffuse at different rates. Warm, salty water above colder, fresher water can have a stable total mass density stratification: the stabilizing temperature difference outweighs the destabilizing salinity difference.^[ref]

A small upper parcel displaced downward enters colder surroundings. It loses heat relatively quickly while retaining more of its salt, becoming denser and continuing downward. A fresher parcel displaced upward can gain heat while remaining relatively fresh and light. The distinction between thermal diffusivity and solutal diffusivity supplies the feedback; stability of the initial combined mass density profile does not exclude this mechanism. The density ratio records the competing contributions, while the salt-finger instability criterion specifies the parameter regime.

A laboratory analog can replace heat and salt by two dissolved substances. David Osmond describes a 1820-by-80-by-120 millimetre tank with salt and sugar solutions entering at opposite ends and an overflow at the centre. The supplied solutions had matching mass density, but salt diffused faster than sugar. The salt-rich plume could lose salt faster than it gained sugar, producing a lighter core and denser surroundings. Fingering and diffusive layers appeared in different regions, showing that identical source densities need not remain dynamically equivalent when composition diffuses.^[ref]

In this analog, salt plays the faster-diffusing role played by heat in the ocean, while sugar plays the slower-diffusing role of oceanic salt. Keeping that correspondence explicit prevents reversing the physical explanation.

An SI prefix supplies an exact decimal factor when attached to a unit of measurement. For example, milli means $10^{-3}$ and micro means $10^{-6}$; a millimetre and a micrometre are correspondingly scaled metres. The prefix symbol and unit symbol form one unit that can itself be raised to a power.^[ref]

For an original conversion example,The area conversion squares the factor as well as the unit. Applying just one factor of $10^{-3}$ to that area would give $0.004{\mathrm{m}}^2$, a value 1000 times too large. Scientific notation makes the power explicit.

Prefix symbols are case-sensitive and cannot be stacked. For mass, prefixes attach to gram, because the base-unit name kilogram already contains a prefix. SI prefixes denote powers of ten, even in a computing context; they do not silently change into powers of two.^[ref] An exact unit conversion scales any stated measurement uncertainty with the value; it does not make an uncertain measurement exact.