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.
Key knowledge
For units connected by a scale factor, multiplying the unit by a factor divides the numerical value by that factor. Celsius temperature values instead require an offset from kelvin values.
Values and equations
1 km = 1000 m
km
Kilometre
m
Metre
Conditions and scope
The scale-factor rule applies to units of the same kind of quantity.
For Celsius values, t/°C = T/K − 273.15; temperature intervals have equal numerical values in K and °C.
Sources · 9
References
Sources retain their recorded scope. A source link alone does not establish verification of every statement.
Bureau International des Poids et Mesures (BIPM)2 sources
SI Brochure 2.3.1 (kelvin/Celsius), chapter 3 and 5.4.1; NIST prefix factors.
2026-10-10 · Scale conversion and Celsius exception only; conversion does not improve the original measurement uncertainty.
Foundational review
2026-10-10 · Fresh primary-source inspection of the complete compact record, including every statement, equation, quantity and material condition, followed by independent AI editorial review. This check does not certify all linked lessons or every passage of every cited publication.
Sources from other places
Scope or convention differs
Celsius numerical values require an offset; kelvin/Celsius intervals have equal numerical values.
The Portuguese standard shares the original BIPM family; it is regional implementation, not independent evidence.
A quantity value combines a number and a reference. For an ordinary unit-based scalar quantity, Q={Q}[Q], where {Q} is its numerical value in unit [Q]. Thus 5.34m and534cm express the same length with different numbers. Not every reference is a unit: specified procedures or reference materials can also define how a value is expressed.
This relation concerns the stated quantity value, numerical value and unit claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
A coherent derived unit, for a stated quantity system and selected base units, is expressed as a product of powers of those base units with numerical factor one. In the SI, m/s is coherent for speed while km/h is a compatible unit requiring a conversion factor. Coherence is a relationship to a unit system; it is not a claim that every permissible unit is coherent.
This relation concerns the stated coherent derived units claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
Relative standard uncertainty is standard uncertainty divided by the absolute measured quantity value. For y≠0, u_r=u(y)/|y|; its percentage form is100u_r%. Near zero, relative uncertainty can become arbitrarily large while absolute uncertainty remains finite. The scale’s zero must have the intended meaning: an offset temperature conversion changes relative ratios even when the same temperature is represented.
This relation concerns the stated relative standard uncertainty claim and its conditions; it does not assert an unqualified prerequisite or an additional theorem.
The minute, hour and day correspond to 60 s, 3600 s and 86400 s. The litre is exactly 10⁻³ m³, the tonne is 1000 kg, and the electronvolt is exactly 1.602176634×10⁻¹⁹ J. These commonly used non-SI units are listed with SI conversions; inclusion gives them no special status within the SI and does not make them coherent SI units. Both l and L are allowed litre symbols.
The numerical equalities instantiate the existing scale-factor conversion principle.
Learning guidance · 3 / 3
Preserved learning suggestions. They are not proof, empirical evidence or mandatory prerequisites.