SI prefix
Enable an agent to recognise an SI prefix, interpret its exact decimal scaling, and judge whether its use in a unit expression is valid.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
recalled by Codex without web access - no source was read
Researched by: Codex
Purpose and description
Enable an agent to recognise an SI prefix, interpret its exact decimal scaling, and judge whether its use in a unit expression is valid.
An SI prefix is an internationally agreed name and symbol placed before a unit name or symbol to form a decimal multiple or submultiple of that unit.
It can be Resolve a name or symbol to a verified SI prefix and its exact decimal exponent.; Validate a prefix-unit combination against the applicable formation rules.; Convert between differently prefixed forms of the same unit while preserving quantity value.; Interpret scaling correctly when a prefixed unit is raised to a power.; Detect ambiguous case, character substitutions, stacked prefixes, and confusion with binary prefixes.; Select a readable prefixed representation subject to domain conventions and destination-system support..
Distinguishing features
An SI prefix denotes an exact power-of-ten multiplier; it does not independently denote a physical quantity or unit.
Its identity requires an authorised name-symbol-factor association, rather than any convenient decimal abbreviation.
Symbol case is significant: m denotes milli and M denotes mega.
SI prefixes differ from binary prefixes: kilo denotes 10^3, whereas kibi denotes 2^10.
A prefix and unit symbol form one unit symbol without an intervening space; an exponent applies to that combined unit.
Scope
+ Canonical prefix names and case-sensitive symbols
+ Exact powers of ten represented by prefixes
+ Rules for attaching prefixes to unit names and symbols
+ Interpretation of prefixes in powered and compound unit expressions
+ Standardisation provenance and support in particular systems
- Definitions and realisations of SI base and derived units
- Measured quantities, observations, and measurement uncertainty
- IEC binary prefixes and their powers-of-two scaling
- General linguistic prefixes and unrelated abbreviations
- Complete grammars for quantity expressions and dimensional analysis
Characteristics
- Canonical name
- Standardised prefix name, with language identified where relevant Supports recognition while separating normative names from translations and informal spellings.
- Canonical symbol
- Exact case-sensitive symbol, such as k, M, m, or μ A case change or character substitution can alter the scale or break recognition.
- Decimal exponent
- Dimensionless signed integer n, giving the exact multiplier 10^n Enables exact conversion without treating the prefix as an approximate numerical value.
- Authorising standard record
- Applicable SI publication or resolution, with edition or date and supporting passage Distinguishes verified SI status from a proposed, historical, or informal modifier.
- Attachment eligibility
- Target unit and applicable prefix-formation rule, including restrictions and exceptions Having a valid prefix does not make every prefix-unit combination valid.
- Implementation support
- Supported, unsupported, partially supported, or unverified in a named parser, format, or system version Separates standards validity from whether a particular tool can correctly process the prefix.
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 5 bundles · 9 layers · 17 findings · 25 questions.
Prefix identity The name, symbol, and exact scaling association that identifies an SI prefix.
An agent must recognise the intended modifier before interpreting or rewriting a quantity expression.
Names and symbols
Canonical forms and the boundaries between authorised symbols and input variants.
Canonical prefix token
Record the prefix's name and exact symbol, preserving case and distinguishing canonical characters from accepted input substitutions.
- What canonical name and case-sensitive symbol identify this prefix in the applicable SI reference? definition
- Which translations, character variants, or ASCII substitutions are encountered, and which may the target system safely normalise? action
Exact decimal scale
The mathematical meaning of the prefix independent of any attached unit.
Power-of-ten association
Represent scaling as an exact integer exponent of ten, distinct from binary scaling or approximate magnitude labels.
- Which integer n defines this prefix's exact multiplier 10^n? measurement
- Does the observed token denote this decimal prefix, a binary prefix, or an informal abbreviation in its context? boundary
Unit formation How a prefix may form a valid unit name or symbol.
Prefix validity depends on attachment rules, including exceptions that simple string concatenation misses.
Attachment rules
Joining a single prefix to an eligible unit without creating an independent unit or stacked prefix.
Single-prefix attachment
Check direct attachment to a unit symbol and distinguish valid prefix formation from standalone or compounded prefix use.
- Which unit does the prefix modify, and does the applicable reference permit that combination? boundary
- Does the expression attach one prefix directly to the unit symbol without a space or another prefix? action
Exception-sensitive formation
Formation rules that require knowledge of the unit rather than the prefix alone.
Mass and unit restrictions
Account for mass prefixes being attached to gram rather than kilogram, and verify prefix permissions for other units rather than assuming universal applicability.
- For a mass expression, has scaling been formed from gram rather than by adding a prefix to kilogram? action
- What documented restriction or convention governs prefix use with this particular SI or non-SI unit? provenance
Scaling and representation Operational interpretation of prefixes within quantity expressions.
Correct recognition must lead to correct arithmetic, especially when units are powered or appear in denominators.
Expression scale
Propagation of a prefix factor through the attached unit's algebraic role.
Powered prefix factor
Treat a prefix as part of its attached unit: for example, cm² carries a factor of 10^-4 relative to m².
- What exponent applies to the prefixed unit, and therefore what total power of ten does this occurrence contribute? measurement
- In a compound expression, which unit factor carries the prefix, and is that factor multiplied, divided, or raised to a power? boundary
Equivalent representation
Changing the prefix while preserving the represented quantity.
Value-preserving rescaling
Adjust the numerical value by the exact ratio of prefix factors, considering unit powers and the desired presentation.
- What exact numerical adjustment preserves the quantity when replacing the original prefix with the target prefix? measurement
- Which valid prefix gives an appropriate presentation under the domain's conventions without implying additional measurement precision? action
Authority and interoperability Evidence of SI status and reliable use across documents and software.
An authorised prefix can still be misread or unsupported, and historical material must be interpreted against an identified reference.
Standardisation evidence
Traceable authority for the name-symbol-factor association and its applicability.
Verified SI status
Anchor recognition to a source actually consulted, identifying the relevant edition or decision rather than inferring status from common usage.
- Which consulted SI publication or CGPM resolution establishes this prefix's name, symbol, and multiplier? provenance
- Which reference date or edition governs interpretation of the document or system being assessed? boundary
Machine and human interpretation
Risks introduced by character handling, parser vocabulary, and contextual ambiguity.
Lossless prefix exchange
Verify that a receiving system preserves the intended symbol and scale, including case-sensitive distinctions and micro-symbol handling.
- Does the named receiving system recognise this prefix and preserve its exact scale when parsing and serialising the expression? action
- Could case folding, character replacement, or confusion with a unit symbol change the interpretation, and what evidence resolves the ambiguity? boundary
Evidence and external alignment What the world already says about this thing, gathered so the model can be checked against it.
A model that cannot be lined up against existing standards, identifiers and practice cannot be adopted by anyone who already uses them.
Reported evidence
Findings from the breadth pass, kept separate from the structural claims.
Check these first
Recalled without web access and unsourced; every item is a lead to verify.
- This describes the metrological sense of SI prefix; no separate sense was supplied.
- Standards and the 2022 extension are recalled, not checked against source documents.
- Which of these check these first hold for the sense of SI prefix this model covers, and on what evidence? provenance
Kinds and varieties
Recalled without web access and unsourced; every item is a lead to verify.
- Prefixes for decimal multiples, such as kilo (10³)
- Prefixes for decimal submultiples, such as milli (10⁻³)
- Which of these kinds and varieties hold for the sense of SI prefix this model covers, and on what evidence? provenance
Identifiers and schemes
Recalled without web access and unsourced; every item is a lead to verify.
- SI prefix names and symbols - Each prefix pairs a name and case-sensitive symbol with a specified power of ten, such as mega, M, 10⁶, or micro, µ, 10⁻⁶. - Symbols are standardized mathematical notation, not abbreviations; case changes can change the factor.
- Which of these identifiers and schemes hold for the sense of SI prefix this model covers, and on what evidence? provenance
Standards and regulation
Recalled without web access and unsourced; every item is a lead to verify.
- BIPM SI Brochure: defines SI prefixes and rules for writing and combining them with units.
- General Conference on Weights and Measures (CGPM), Resolution 3 of its 27th meeting (2022): introduced ronna, quetta, ronto and quecto.
- ISO 80000-1, issued by ISO: gives general rules for quantities, units and their notation.
- Which of these standards and regulation hold for the sense of SI prefix this model covers, and on what evidence? provenance
Real-world use
Recalled without web access and unsourced; every item is a lead to verify.
- Expressing large and small measurements conveniently, such as kilometres, milligrams and nanoseconds.
- Scaling engineering specifications, instrument displays and scientific results.
- Expressing decimal data quantities and rates, such as megabytes and gigabits per second.
- Which of these real-world use hold for the sense of SI prefix this model covers, and on what evidence? provenance
Typical measurements
Recalled without web access and unsourced; every item is a lead to verify.
- Multiplicative scale factor - Discrete factors from 10⁻³⁰ to 10³⁰; available exponents are ±1, ±2 and multiples of three from ±3 through ±30. - Dimensionless
- Which of these typical measurements hold for the sense of SI prefix this model covers, and on what evidence? provenance
Failure modes and hazards
Recalled without web access and unsourced; every item is a lead to verify.
- Confusing case-sensitive symbols, such as m for milli and M for mega, causes large scaling errors.
- Treating kilo, mega or giga as powers of two instead of powers of ten creates discrepancies in data quantities.
- Ignoring that an exponent applies to the prefixed unit gives incorrect area or volume conversions: 1 cm² equals 10⁻⁴ m².
- Stacking prefixes violates SI rules; mass multiples and submultiples are formed by attaching a prefix to gram, rather than kilogram.
- Loss or substitution of the micro symbol in transcription or software can obscure a unit and cause scaling errors.
- Which of these failure modes and hazards hold for the sense of SI prefix this model covers, and on what evidence? provenance
Regional variation
Recalled without web access and unsourced; every item is a lead to verify.
- Prefix symbols and factors are internationally standardized; written names can vary with language.
- Which of these regional variation hold for the sense of SI prefix this model covers, and on what evidence? provenance
Neighbouring kinds and how to tell them apart
Recalled without web access and unsourced; every item is a lead to verify.
- Unit of measurement - A unit supplies a reference for measuring a quantity; a prefix supplies only a scaling factor and is not used independently.
- Binary prefix - Binary prefixes such as kibi and mebi denote powers of two; SI prefixes denote powers of ten.
- Scientific notation - Scientific notation writes an explicit power of ten with a number; an SI prefix incorporates a prescribed power of ten into a unit name or symbol.
- Which of these neighbouring kinds and how to tell them apart hold for the sense of SI prefix this model covers, and on what evidence? provenance
What the second pass must settle
- Which authoritative SI edition and resolutions will be consulted to establish the complete prefix inventory and adoption history?
- Which language-specific prefix spellings should be recognised, and which authority governs each spelling?
- Which Unicode variants and ASCII substitutions should target systems accept for micro while preserving a canonical representation?
- Which unit-specific permissions and restrictions must be included for the intended application, especially for non-SI units?
- Which destination parsers and data formats must be checked for prefix coverage, case preservation, and correct handling of powered units?