View source for User:PL290/MoS/Numbers

==Numbers as figures or words==
{{shortcut|WP:ORDINAL}}
As a general rule, in the body of an article, single-digit whole numbers from zero to nine are spelled out in words; numbers greater than nine are commonly rendered in numerals, or in words if they are expressed in one or two words ({{xt|16}} or {{xt|sixteen}}, {{xt|84}} or {{xt|eighty-four}}, {{xt|200}} or {{xt|two hundred}}, but {{xt|3.75}}, {{xt|544}}, {{xt|21&nbsp;million}}). This applies to [[Ordinal numbers (linguistics)|ordinal numbers]] as well as [[English numerals|cardinal numbers]]. However there are frequent exceptions to these rules.
*In [[Table (information)|table]]s and [[Help:Infobox|infobox]]es, quantitative data is expressed as numerals; numerals will also fit better in  limited space. Numbers within a table's explanatory text and comments should be consistent with the general rule.
*Comparable quantities should be all spelled out or all figures: we may write either {{xt|5 cats and 32 dogs}} or {{xt|five cats and thirty-two dogs}}, not {{!xt|five cats and 32 dogs}}.
*Adjacent quantities which are not comparable should usually be in different formats: {{xt|twelve 90-minute volumes}} or {{xt|12 ninety-minute volumes}} is more readable than {{!xt|12 90-minute volumes}} or {{!xt|twelve ninety-minute volumes}}.
*Numbers that begin a sentence are spelled out, since using figures risks the period being read as a decimal point or abbreviation mark; it is often better to recast the sentence than to simply change format, which may produce other problems; e.g., do not use {{!xt|Nineteen forty five and 1950 were important elections for the Labour Party}}, but rather {{xt|The elections of 1945 and 1950 were important for the Labour Party.}}
*The numerical elements of dates and times are not normally spelled out (that is, do not use {{!xt|the seventh of January}} or {{!xt|twelve forty-five p.m.}} or {{!xt|Two thousand eight was the year that ...}} ). However, they should be spelled out where customary in historical references such as {{xt|[[Seventh of March Speech]]}} and {{xt|[[Fifth of November]]}}; these are treated as proper names. 
*Centuries are given in figures: {{xt|the 5th century BCE}}; {{xt|19th-century painting}}. 
*Simple fractions are normally spelled out; use the fraction form if they occur in a percentage or with an abbreviated unit ({{xt|{{frac|1|8}} mm}} or {{xt|an eighth of a millimeter}}, but not {{!xt|an eighth of a mm}}) or if they are mixed with whole numerals.
*Decimal representations containing a decimal point are not spelled out ({{xt|1.00}}, {{xt|3.14159}}).
*Numbers in [[mathematical formula]]e are never spelled out ({{xt|3&nbsp;<&nbsp;π&nbsp;<&nbsp;22/7}}, '''not''' {{!xt|three < π < 22 sevenths}}).
*Do not use spelled-out numbers before symbols for units of measurement: write {{xt|five minutes}}, {{xt|5 minutes}}, or {{xt|5&nbsp;min}}, ''but not'' {{!xt|five&nbsp;min}}.
*Measurements, stock prices, and other quasi-continuous quantities are normally stated in figures, even when the value is a small positive integer: {{xt|9 mm}}, {{xt|The option price fell to 5 within three hours after the announcement}}.
* When expressing large approximate quantities, it is preferable to write them spelled out, or partly in figures and part as a spelled{{nbhyph}}out named number; e.g., {{xt|one hundred thousand troops}} may be preferable to {{xt|100,000 troops}} when the size of the force is not known exactly; write {{xt|Japan has the world's tenth largest population, with about 128&nbsp;million people}} (as it is just an approximation to a number likely to be anywhere between 127,500,000 and 128,500,000), but {{xt|The movie grossed $28,106,731 on its opening day}} (the exact quantity).
* When both a figure and spelled-out named number are used in a quantity, it is useful to use a non-breaking space, as in <code>128&amp;nbsp;million</code> or <code>128<nowiki>{{nbsp}}</nowiki>million</code> to prevent a line break from occurring between them.
* Sometimes figures and words may carry different meanings, for example {{xt|Every number except one}} implies that there is one exception (we don't know which), while {{xt|Every number except 1}} means that the specific number 1 is the exception.
* Proper names, formal numerical designations, and other idioms comply with common usage; e.g., write {{xt|Chanel No. 5}}, {{xt|4 Main Street}}, {{xt|1-Naphthylamine}}, {{xt|Channel 6}}, {{xt|Fourth Amendment}}, {{xt|Seventeenth Judicial District}}, {{xt|Seven Years' War}}. This is the case even where it causes a numeral to open a sentence, although this is usually avoided by rewording.

==Typography==
*Spelled-out two-word numbers from 21 to 99 are hyphenated ({{xt|fifty-six}}), as are fractions used as adjectives ({{xt|seven-eighths}}). Do not hyphenate other multi-word numbers ({{xt|five hundred}}, not {{!xt|five-hundred}}).
*Where a whole number in a [[percentage]] is spelled out, the [[percent sign]] is not used ({{xt|three percent}} or {{xt|3%}}, not {{!xt|three %}}).
*The ordinal suffix (e.g., ''th'') is not [[superscript]]ed ({{xt|23rd}} and {{xt|496th}}, not {{!xt|23<sup>rd</sup>}} and {{!xt|496<sup>th</sup>}}).

==Delimiting (grouping of digits)==
* Numbers with five or more digits to the left of the decimal point (i.e., 10,000 or more) should be delimited into groups so they can be easily parsed, such as by using [[Decimal separator#thousands separator|commas]] every three digits; e.g., {{xt|12,200}} and {{xt|255,200}} and {{xt|8,274,527}} etc.
* Numbers with four digits to the left of the decimal point may or may not be delimited; that is, {{xt|there were 1250 head of cattle}} and {{xt|there were 1,250 head of cattle}} are both acceptable.
* Numbers are not delimited when they are part of mailing and shipping addresses, page numbers, and years with four or fewer digits; years with five or more digits should be delimited (e.g. {{xt|10,400&nbsp;BC}}).
* In scientific articles, particularly those directed to an expert readership, numbers may be delimited with thin spaces using the {{tl|gaps}} template. Coding <code><nowiki>{{gaps|8|274|527}}</nowiki></code> produces {{xt|{{gaps|8|274|527}}}} (note: the thin space character and its [[SGML entity|HTML entity]], <code>&amp;thinsp;</code>, do not render correctly on some browsers or on [[screen reader]]s used by visually impaired people).
* The style of delimiting numbers to the left of the decimal point must be consistent throughout an article.
* Constants in mathematics-oriented articles may be grouped in fives; e.g., {{xt|{{gaps|3.14159|26535|89793|23846|26433|83279|...}}}}.
* Numbers with more than four digits to the right of the decimal point, particularly those in engineering and science where distinctions between different values are important, may be separated (delimited) into groups using the {{tl|val}} template, which uses character-positioning techniques rather than distinct characters to form groups. According to [[International Organization for Standardization|ISO]] convention (observed by the [[NIST]] and the [[BIPM]]), it is customary to not leave a single digit at the end, so the last group comprises two, three, or four digits. 

:The recommended progression on Wikipedia is  as follows: {{xt|{{val|1.123}}}}, {{xt|{{val|1.1234}}}}, {{xt|{{val|1.12345}}}}, {{xt|{{val|1.123456}}}}, {{xt|{{val|1.1234567}}}}, {{xt|{{val|1.12345678}}}}, {{xt|{{val|1.123456789}}}}, etc. The <nowiki>{{val}}</nowiki> template handles these grouping details automatically; e.g., <code><nowiki>{{val|1.1234567}}</nowiki></code> generates {{xt|{{val|1.1234567}}}} (with a four-digit group at the end); it can parse no more than a total of 15 significant digits in the [[significand]]. For significands longer than this, editors should delimit high-precision values using the {{tl|gaps}} template; e.g., <code><nowiki>{{gaps|1.234|567|890|123|456}}</nowiki></code> → {{xt|{{gaps|1.234|567|890|123|456}}}}.

==Large numbers==
{{See also|Order of magnitude|Long and short scales}}
*Large round numbers are generally assumed to be approximations; only where the approximation could be misleading is it necessary to qualify with words such as ''about''.
*Avoid excessively precise values where they are unlikely to be stable or accurate, or where the precision is unnecessary in the context. The sentence {{xt|The speed of light in a vacuum is 299,792,458 metres per second}} may well be appropriate since it is precisely that value; {{!xt|The distance from the Earth to the Sun is 149,014,769 kilometres}} and {{!xt|The population of Cape Town is 2,968,790 people}} would usually not be, because both values are unstable at that level of precision, and readers are unlikely to care in the context.
*[[Scientific notation]] (e.g., {{xt|{{val|5.8|e=7|u=kg}}}}) is preferred in scientific contexts; editors can use the {{tl|val}} template, which generates such expressions with the syntax <code><nowiki>{{val|5.8|e=7|u=kg}}</nowiki></code>. 
*Where values in the millions occur a number of times through an article, upper-case ''M'' may be used for ''million'', unspaced, after spelling out the first occurrence (e.g., {{xt|She bequeathed her fortune of £100&nbsp;million unequally: her eldest daughter received £70M, her husband £18M, and her three sons £4M each.}}).
*The named numbers [[billion]] and [[trillion]] are understood to be ''short scale'', 10<sup>9</sup> and 10<sup>12</sup> respectively (see [[Long and short scales]]). After the first occurrence in an article, ''billion'' may be abbreviated to unspaced ''bn'' ({{xt|$35bn}}). The prefixes ''giga-'', ''tera-'', and larger and their symbols G, T, ... should be limited to computing and scientific contexts.

==Fractions==
The template {{tl|frac}} is available for representing common fractions. For {{frac|p|q}}, type <nowiki>{{frac|p|q}}</nowiki>. For {{frac|N|p|q}}, type <nowiki>{{frac|N|p|q}}</nowiki>. When copied and pasted, {{frac|N|p|q}} will appear as N+p/q.

==Decimal points==
*A [[decimal separator|decimal point]] is used between the integer and the fractional parts of a decimal; a comma is never used in this role ({{xt|6.57}}, not {{!xt|6,57}}).
*The number of decimal places should be consistent within a list or context ({{xt|The response rates were 41.0 and 47.4 percent, respectively}}, not {{!xt|The response rates were 41 and 47.4 percent, respectively}}), except if the quantities were measured with different precisions.
*Numbers between −1 and +1 require a leading zero ({{xt|0.02}}, not {{!xt|.02}}); exceptions are sporting performance averages ({{xt|.430 [[batting average]]}}) and commonly used terms such as {{xt|[[.22 caliber]]}}.

==Percentages==
*''Percent'' or ''per cent'' are commonly used to indicate percentages in the body of an article. The symbol ''%'' is more common in scientific or technical articles and in complex listings.
*The symbol is unspaced ({{xt|71%}}, not {{!xt|71 %}}).
*In tables and infoboxes, the symbol ''%'' is normally preferred to the spelled-out ''percent'' or ''per cent''. 
*Ranges are preferably formatted with one rather than two percentage signifiers ({{xt|22–28%}}, not {{!xt|22%–28%}}). 
*Avoid ambiguity in expressing a change of rates. This can be done by using [[percentage point]]s, not percentages, to express a change in a percentage or the difference between two percentages; for example, {{xt|The agent raised the commission by five percentage points, from 10 to 15%}} (if the 10% commission had instead been raised by 5%, the new rate would have been 10.5%). It is often possible to recast the sentence to avoid the ambiguity ({{xt|made the commission larger by half.}}). ''Percentage point'' should not be confused with ''[[basis point]]'', which is a hundredth of a percentage point.

==Natural numbers==
(tag removed) mergeto|Manual of Style (mathematics)}}
The [[set (mathematics)|set]] of [[natural numbers]] has two common meanings: {0, 1, 2, 3, ...}, which may also be called ''non-negative integers'', and {1, 2, 3, ...}, which may also be called ''positive integers''. Use the sense appropriate to the field to which the subject of the article belongs if the field has a preferred convention. If the sense is unclear, and if it is important whether or not zero is included, consider using one of the alternative phrases rather than ''natural numbers'' if the context permits.

==Repeating decimals==
The preferred way to indicate a repeating decimal is to place a bar over the digits that repeat. To achieve this the template {{tl|overline}} can be used. For example, the markup <code><nowiki>14.{{overline|285714}}</nowiki></code> gives ''14.{{overline|285714}}''.

Consider a short explanation of the notation the first time this notation is used in an article. Some authors place the repeating digits in parentheses rather than using an overbar (perhaps because overbars are not available in their typesetting environment) but this should be avoided in Wikipedia to avoid confusion with expressing uncertainty.

==Non-base-10 notations==
For numbers expressed in [[base (mathematics)|bases]] other than base ten:
*In computer-related articles, use the [[C (programming language)|C programming language]] prefixes ''0x'' (zero-ex) for hexadecimal and ''0'' (zero) for octal. <!-- Note that 0b is *not* a valid C prefix --> For binary, use ''0b''. Consider including a note at the top of the page about these prefixes.
*In all other articles, use subscript notation. For example: ''137<sub>9</sub>'', ''241<sub>6</sub>'', ''2A9<sub>12</sub>'', ''A87D<sub>16</sub>'' (use <code>&lt;sub></code> and <code>&lt;/sub></code>).
*For base eleven and higher, use whatever symbols are conventional for that base. One quite common convention, especially for base 16, is to use upper-case A&ndash;F for digits from 10 through 15 (''0x5AB3'').

==Scientific notation, engineering notation, and uncertainty==
===Notations===
* The template {{tl|val}} can be used to facilitate the generation of scientific notation. It is a flexible tool that allows editors great latitude and must have arguments (each section between the vertical bars) properly entered in order for it to generate output that is compliant with formating conventions.
* [[Scientific notation]] is done in the format of one leading digit/decimal marker/rest of digits/×10<sup>''n''</sup>, where ''n'' is the integer that gives one leading digit.
** {{xt|{{val|1.602|e=-19}}}} is a proper use of scientific notation.
** {{!xt|{{val|160.2|e=-17}}}} is not a proper use of scientific notation.
* [[Engineering notation]] is done in the format of leading digits/decimal marker/rest of digits/×10<sup>''n''</sup>, where ''n'' is a multiple of 3. The number of leading digits is adjusted accordingly.
** {{xt|{{val|132.23|e=6}}}} is a proper use of engineering notation.
** {{!xt|{{val|1.3223|e=8}}}} is a not proper use of engineering notation.
* It is clearer to avoid mixing scientific notation and engineering notation in the same context (e.g., do not write {{!xt|A {{val|2.23|e=2|u=m2}} region covered by {{val|234.0|e=6|u=grains of sand}}}}).
* Use discretion when it comes to using scientific and engineering notation. Not all values need to be written in it.
** Sometimes it is useful to compare values with the same power of 10 (often in tables) and scientific or engineering notation might not be appropriate.

===Uncertainty===
* Uncertainties can be written in various ways:
** Value/±/uncertainty/×/10<sup>n</sup>/unit symbol (e.g., {{val|1.534|0.35|e=23|u=m}})
*** Do not group value and uncertainty in parenthesis before the multiplier (e.g., do not write (15.34&nbsp;±&nbsp;0.35)&nbsp;×&nbsp;10<sup>23</sup>&nbsp;m)
** Value/superscript positive uncertainty/subscript negative uncertainty/×/10<sup>n</sup>/unit symbol (e.g., {{val|15.34|+0.43|-0.23|e=23|u=m}})
** Value(uncertainty in the last digits)/×/10<sup>n</sup>/unit symbol (e.g., {{val|1.604|(48)|e=-4|u=J}})
** Value/±/relative uncertainty(percent)/unit symbol (e.g., 12.34&nbsp;±&nbsp;5%&nbsp;m<sup>2</sup>)
* The template {{tl|val}} may be used to automatically handle all of this.