Foundations

Describe a quantity as a numerical value with a unit, and distinguish its physical kind from its dimension. Build length, area, volume and rate units, check meaningful combinations, and separate exact unit relations from measurement uncertainty.

Convert quantities with exact unit ratios, track cancellation through compound units, and apply the correct powers to area and volume. Distinguish temperature readings from differences, check dimensions and context, and retain measurement uncertainty when reporting.

c denotes the speed of light in vacuum. Its numerical value is fixed exactly in SI units.

h denotes the Planck constant. Its numerical value is fixed exactly in SI units.

ΔνCs denotes the unperturbed ground-state hyperfine transition frequency of caesium-133. Its numerical value is fixed exactly in SI units.

Seven named base units organize the SI quantity system.

Prefix symbols specify decimal scale factors.

Use dimensions to detect impossible quantity equations.

The elementary charge has an exact SI numerical value.

The Boltzmann constant has an exact SI numerical value.

The mole is linked to a specified number of entities.

A specified frequency fixes the photometric SI reference.

Equal dimensions do not make quantities interchangeable.

A numerical value depends on the chosen unit.

Coherence means no extra numerical factor in the base-unit product.

Ordering and category labels do not justify ordinary arithmetic.

A solid angle measures a cone of directions rather than a plane rotation.

Optical power, directional power and surface densities are different quantities.

Photometry weights radiation with a specified standard visual response.

Symbol form, spacing and parentheses preserve the meaning of reported quantities.

Mass prefixes attach to gram even though kilogram is the SI base unit.

Common non-SI unit names require their correct SI scale factors.