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{{short description|Converting a measuring system to a decimal base}}
{{About|decimalisation of currency and measurement|the system of library classification|Dewey Decimal Classification|the development of the number system|Decimal}}
'''Decimalisation''' or '''decimalization''' (see [[American and British English spelling differences|spelling differences]]) is the conversion of a system of currency or of weights and measures to units related by [[Power of 10|powers of 10]].

Most countries have decimalised their currencies, converting them from non-decimal sub-units to a [[decimal]] system, with one basic currency unit and sub-units that are valued relative to the basic unit by a power of [[10 (number)|10]], most commonly 100 and exceptionally 1000, and sometimes at the same time, changing the name of the currency and/or the conversion rate to the new currency. 

Today, only two countries have ''de jure'' non-decimal currencies, these being [[Mauritania]] (where 1 [[Mauritanian ouguiya|ouguiya]] = 5 [[khoums]]) and [[Madagascar]] (where 1 [[Malagasy ariary|ariary]] = 5 [[iraimbilanja]]): <ref>{{Cite web|url=http://famouswonders.com/malagasy-ariary/|title=Malagasy Ariary|website=Famous Wonders|date=4 April 2011|access-date=2016-12-13}}</ref> however, these currencies are ''de facto'' decimal as the value of both currencies' main unit is now so low that the sub-units are too small to be of any practical use, and coins of these sub-units are no longer used.  

[[Russia]] was the first country to convert to a decimal currency when it decimalised under Tsar [[Peter the Great]] in 1704, resulting in the silver [[Russian ruble|ruble]] being equal to 100 copper [[kopek]]s.<ref>{{Cite web|url=http://numismatics.org/pocketchange/peter/|title=The Reign of Peter the Great as Represented in the ANS Collection |website=Pocket Change |publisher=[[American Numismatic Society]] |date=12 November 2020}}</ref><ref name=":0">''Encyclopædia Britannica''. 15th ed.<!--assumed based on date – CD-ROM edition?--> Volume 25. 1994.</ref>{{page needed<!--don't actually need page – name of entry is enough-->|date=December 2024}}

For weights and measures, this is also called [[metrication]], replacing traditional units that are related in other ways, such as those formed by successive doubling or halving, or by more arbitrary [[conversion factor]]s. Units of physical measurement, such as length and mass, were decimalised with the introduction of the [[metric system]], which has been adopted by almost all countries (with the prominent exceptions of the [[Metrication in the United States|United States]], and, to a lesser extent, the [[United Kingdom]] and [[Canada]]). Thus, a kilometre is 1,000 metres, while a mile is 1,760 yards. [[Electrical units]] are decimalised worldwide. 

Common [[units of time]] remain undecimalised. Although an [[French Republican calendar|attempt to decimalise them]] was made during the [[French Revolution]], this proved to be unsuccessful and was quickly abandoned.

== Currency decimalisation by region ==
{{see also|List of circulating currencies}}
Decimal currencies have sub-units based on a power of 10. Most sub-units are one-[[100 (number)|100]]th of the base currency unit, but currencies based on [[1000 (number)|1,000]] sub-units also exist in several Arab countries.

Some countries changed the name of the base unit when they decimalised their currency, including:

{| class="wikitable"
|+Examples of currency decimalisation
|-
!scope="col"| New unit
!scope="col"| =
!scope="col"| ×
!scope="col"| Old unit
!scope="col"| Year
|-
| [[German gold mark]]
| =
| {{frac|1|3}}
| [[Vereinsthaler]]
| 1873
|-
| [[Danish krone]]
| =
| {{frac|1|2}}
| [[Danish rigsdaler]]
| 1875
|-
| [[South African rand]]
| =
| {{frac|1|2}}
| [[South African pound]]
| 1961
|-
| [[Australian dollar]]
| =
| {{frac|1|2}}
| [[Australian pound]]
| 1966
|-
| [[New Zealand dollar]]
| =
| {{frac|1|2}}
| [[New Zealand pound]]
| 1967
|-
| [[Fijian dollar]]
| =
| {{frac|1|2}}
| [[Fijian pound]]
| 1969
|-
| [[Nigerian naira]]
| =
| {{frac|1|2}}
| [[Nigerian pound]]
| 1973
|}

===Europe===
In 1534 the [[kopek]] of [[Novgorod Land|Novgorod]] was equated to 1/100 of the [[Russian ruble|ruble]] of [[Principality of Moscow|Moscow]], thus making the Russian ruble Europe's first decimal currency. In the 18th century were introduced the coins {{Transliteration|ru|[[grivennik]]}} (10 kopeks) and [[imperial (coin)|imperial]] (10 rubles). This was not quite decimal currencies as they are known today, as there were smaller units beneath the kopek itself: the [[denga]] (half a kopek, or 200 to the ruble) and the [[polushka]] (half a denga, one-quarter kopek, or 400 to the ruble). After the [[October Revolution]], the [[Soviet Union]] transitioned to a purely decimal model by eliminating the non-decimal subdivisions of the kopek.

[[France]] introduced the [[franc]] in 1795 to replace the [[livre tournois]],<ref>Gadoury, V. ''Monnaies Françaises'' p.48 (1999)</ref> abolished during the [[French Revolution]]. France introduced decimalisation in a number of countries that it invaded during the [[Napoleon I of France|Napoleonic period]].

The [[Dutch guilder]] decimalised in 1817, becoming equal to 100 centen (instead of 20 [[stuiver]]s = 160 [[duit]]en = 320 penningen), with the last pre-decimal coins withdrawn from circulation in 1848.

[[Sweden]] introduced decimal currency in 1855. The [[riksdaler]] was divided into 100 [[öre]]. The riksdaler was renamed the [[Swedish krona|krona]] in 1873.

The [[Austro-Hungarian Empire]] decimalised the [[Austro-Hungarian gulden|gulden]] in 1857, concurrent with its transition from the [[Conventionsthaler]] to the [[Vereinsthaler]] standard.

[[Spain]] introduced its decimal currency unit, the [[Spanish peseta|peseta]], in 1868, replacing all previous currencies.

[[Cyprus]] decimalised the [[Cypriot pound]] in 1955, which comprised 1000 mils, later replaced by 100 cents.

The [[United Kingdom]] (including its overseas territories) and [[Republic of Ireland|Ireland]] decimalised [[pound sterling|sterling]] and the [[Irish pound]], respectively, in 1971. (See [[£sd]] and [[Decimal Day]].)

[[Malta]] decimalised the [[Maltese lira|lira]] in 1972.

===The Americas===

==== North America ====
===== United States =====
Decimalisation was introduced into the [[Thirteen Colonies]] by the [[American Revolution]], and then enshrined in US law by the [[Coinage Act of 1792]].

===== Canada =====
Decimalisation in Canada was complicated by the different jurisdictions before Confederation in 1867. In 1841, the united [[Province of Canada]]'s Governor General, [[Charles Poulett Thomson, 1st Baron Sydenham|Lord Sydenham]], argued for establishment of a bank that would issue dollar currency (the [[Canadian dollar]]). [[Francis Hincks]], who would become the Province of Canada's Prime Minister in 1851, favoured the plan. Ultimately the provincial assembly rejected the proposal.<ref>McCulloch, A. B. "Currency Conversion in British North America, 1760–1900". ''Archivaria'' 16, (Summer 1983): 83–94.</ref> In June 1851, the Canadian legislature passed a law requiring provincial accounts to be kept decimalised as dollars and cents. The establishment of a [[Bank of Canada|central bank]] was not touched upon in the 1851 legislation. The British government delayed the implementation of the currency change on a technicality, wishing to distinguish the Canadian currency from the United States' currency by referencing the units as "Royals" rather than "Dollars".<ref name="Canadian Mint 2003">Canadian Mint. "Currency Reforms, 1841–71". ''A History of the Canadian Dollar''. Ottawa: Canadian Mint, 2003.</ref> The British delay was overcome by the Currency Act of 1 August 1854. In 1858, coins denominated in cents and imprinted with "Canada" were issued for the first time.

Decimalisation occurred in:<ref name="Canadian Mint 2003"/>

{| class="wikitable" border="1"
|-
!
! Date
! Notes
|-
| [[Province of Canada]]
| 1 August 1854
|
|-
| Nova Scotia
| 1 July 1860
| Ordered its first coinage in 1860, but the coins were not shipped by the Royal Mint until 1862
|-
| New Brunswick
| 1 November 1860
| Like Nova Scotia, the coins were received in 1862
|-
| Newfoundland
| 1866
| Took effect in early 1865 and had different coinage from 1865 to 1947
|-
| Vancouver Island
| 1863
|
|-
| British Columbia
| 1865
|
|-
| Manitoba
| 1870
|
|-
| Prince Edward Island
| 1871
|
|}

The colonial elite, the main advocates of decimalisation, based their case on two main arguments.<ref>Mushin, Jerry. "Twentieth Century Currency Reforms: A Comment". ''Kyklos'' 50 (1997): 247–249.</ref> The first was for facilitation of trade and economic ties with the United States, the colonies' largest trading partner; the second was to simplify calculations and reduce accounting errors.<ref>W. T. Easterbrook and Hugh G. J. Aitken, ''Canadian Economic History'' (Toronto: University of Toronto Press, 1988), 381.</ref>

===== Mexico =====
The [[Mexican peso]] was formally decimalised in the 1860s with the introduction of coins denominated in centavos; however, the currency did not fully decimalise in practice immediately and pre-decimal reales were issued until 1897.

===== Bermuda =====
Bermuda decimalised in 1970, by introducing the [[Bermudian dollar]] equal to 8 shillings 4 pence (100 pence, effectively equal to the US dollar under the [[Bretton Woods system]]).

====Caribbean====
* The [[Cuban peso]] decimalised in 1869 (became equal to 100 centavos instead of 8 reales).
* The [[Dominican peso]] decimalised in 1877 (became equal to 100 centavos instead of 8 reales).
* The [[Haitian gourde]] decimalised in 1881 by peg to French franc (became equal to 100 centimes/santim).
* The [[Netherlands Antillean guilder]] decimalised in 1892 by peg to Dutch guilder (became equal to 100 centen).
* The [[British West Indies dollar]] decimalised in 1955.
* The [[Jamaican dollar]] decimalised in 1969.

==== Central America ====

*[[Costa Rican peso]] decimalised in 1864, divided into 100 centavos, instead of 8 reales.
*[[Honduran peso]] decimalised in 1871, divided into 100 centavos, instead of 8 reales.
*[[Belize dollar|British Honduran (Belize) dollar]] decimalised in 1885, divided into 100 cents.

==== South America ====
* The [[Venezuelan peso]] decimalised in 1843.
* The [[Colombian peso]] decimalised in 1847 (became equal to 10 décimos instead of 8 reales, later became equal to 100 centavos).
* The [[Chilean peso (1817–1960)|Chilean peso]] decimalised in 1851 (became equal to 10 décimos or 100 centavos instead of 8 reales).
* The [[Currency_of_Uruguay#1863–1875_Peso_and_Doblón, 1817–1960|Uruguayan peso]] decimalised in 1863.
* The [[Peruvian sol (1863–1985)|Peruvian sol]] decimalised in 1863 (equal to 10 dineros or 100 centavos).
* The [[Paraguayan peso]] decimalised in 1870 (became equal to 100 centésimos, later centavos, instead of 8 reales).
* The [[Ecuadorian peso]] decimalised in 1871.
* The [[Argentine peso moneda nacional|Argentine peso]] decimalised in 1881.

===Africa===
* The [[Ethiopian birr]] decimalised in 1931 (became equal to 100 metonnyas instead of 16 ghersh).
* The [[Ghanaian cedi]] decimalised in 1965.
* The [[Zambian kwacha]] decimalised in 1968.
* The [[Rhodesian dollar]] decimalised in 1970.
* The [[Gambian dalasi]] decimalised in 1971.
* The [[Malawian kwacha]] decimalised in 1971.
* The [[Nigerian naira]] decimalised in 1973.

==== South Africa ====
The [[South African rand|rand]] was introduced on 14 February 1961. A Decimal Coinage Commission had been set up in 1956 to consider a move away from the denominations of pounds, shillings and pence, submitting its recommendation on 8 August 1958.<ref>Mboweni, T.T. 2001. The Reserve Bank and the Rand: some historic reflections. Speech by the Governor of the Reserve Bank 29 Nov 2001. http://www.reservebank.co.za</ref> It replaced the [[South African pound]] as legal tender, at the rate of 2 rand = 1 pound or 10 [[shilling]]s to the rand. Australia, New Zealand and [[Rhodesia]] also chose ten shillings as the base unit of their new currency.

===Oceania===

==== Australia and New Zealand ====
[[File:ABC Decimal Currency.ogv|thumb|right|1964 [[Australian Broadcasting Corporation|ABC]] report describing the design of the soon to be introduced Australian decimal coins]]
[[Australia]] decimalised on 14 February 1966, with the [[Australian dollar]]s replacing the [[Australian pound]]. A television campaign containing a memorable [[jingle]], sung to the tune of "[[Click Go the Shears]]", was used to help the public to understand the changes.<ref>{{Cite web|url = https://www.youtube.com/watch?v=TZVEEs-RJpw|title = Australian Dollar Bill Currency Decimal Jingle from 1965|website = [[YouTube]]}}</ref> [[New Zealand]] decimalised on 10 July 1967, with the [[New Zealand dollar]]s replacing the [[New Zealand pound]].

In both countries, the conversion rate was one pound to two dollars and 10 shillings to one dollar.
{| class="wikitable"
|+Conversion between £sd and $c, Australia and New Zealand
!£sd
!$c
|-
|£50
|$100
|-
|£10
|$20
|-
|£5
|$10
|-
|£1
|$2
|-
|10/–
|$1
|-
|5/–
|50c
|-
|2/–
|20c
|-
|1/–
|10c
|-
|6d
|5c
|-
|3d
|2.5c
|-
|1.2d
|1c
|-
|1d
|{{Frac|5|6}}c
|}
To ease the transition, the new 5-cent, 10-cent and 20-cents coins were the same size and weight, and the new $1, $2, $10 and $20 banknotes (and the new $100 banknote in New Zealand) were the same colour, as their pre-decimal equivalents. Because of the inexact conversion between cents and pence, people were advised to tender halfpenny, penny and threepence coins in multiples of sixpence (the [[Least common multiple|lowest common multiple]] of both systems) during the transition.<ref>{{Cite web|url=https://museum.rba.gov.au/displays/rba-currency-reform/|title=The Reserve Bank and Reform of the Currency: 1960–1988|url-status=dead|archive-url=https://web.archive.org/web/20190315121444/https://museum.rba.gov.au/displays/rba-currency-reform/|archive-date=2019-03-15}}</ref>

==== Rest of Oceania ====

*[[Tongan pa'anga]] decimalised on 3 April 1967
*[[Samoan tala]] decimalised on 10 July 1967
*[[Fijian dollar]] decimalised on 15 January 1969

===Asia===

King [[Chulalongkorn]] decimalised the [[Thai baht|Thai currency]] in 1897. The tical (baht) is now divided into one hundred satang.
{| class="wikitable"
|+
!Baht
!Feuang
!Att
!Bia
! rowspan="5" |> Decimalization >
!Baht
!Satang
|-
|'''1'''
|8
|64
|6400
| rowspan="4" |'''1'''
| rowspan="4" |100
|-
|1/8
|'''1'''
|8
|800
|-
|1/64
|1/8
|'''1'''
|100
|-
|1/6400
|1/64
|1/100
|'''1'''
|}
[[Iran]] decimalised its currency in 1932, with the [[Iranian rial|rial]], subdivided into 100 new dinars, replacing the [[Iranian qiran|qiran]] at par.

[[Saudi Arabia]] decimalised the [[Saudi riyal|riyal]] in 1963, with 1 riyal = 100 halalas. Between 1960 and 1963, the riyal was worth 20 [[kuruş|qirsh]], and before that, it was worth 22 qirsh.

The [[Yemen Arab Republic]] introduced the coinage system of 1 [[North Yemeni rial]] = 100 [[fils (currency)|fils]] in 1974, to replace the 1 rial = 40 buqsha = 80 halala = 160 zalat system. The country was one of the last to convert its coinage.

[[Japan]] historically had two decimal subdivisions of the yen: the sen (1/100) and the rin (1/1,000). However, they were taken out of circulation as of December 31, 1953, and all transactions are now conducted in multiples of 1 yen.<ref>{{cite web|url=http://law.e-gov.go.jp/htmldata/S62/S62HO042.html|title=通貨の単位及び貨幣の発行等に関する法律|work=e-gov.go.jp|access-date=2014-05-26|archive-url=https://web.archive.org/web/20130208174436/http://law.e-gov.go.jp/htmldata/S62/S62HO042.html|archive-date=2013-02-08|url-status=dead}}</ref>

==== Rupee-anna-pice-pie to Rupee-paisa conversion ====

[[India]] changed from the [[rupee]], [[Anna (coin)|anna]], [[Pie (Indian coin)|pie]] system to decimal currency on 1 April 1957. [[Pakistan]] decimalised [[Pakistani rupee|its currency]] in 1961.

In India, Pakistan, and other places under British colonization where a system of 1 rupee = 16 [[Indian anna|anna]] = 64 pice (old paisa) = 192 pie was used, the decimalisation process defines 1 rupee = 100 naya (new) paisa. The following table shows the conversion of common denominations of coins issued in modern India and Pakistan. 

*'''Bold''' denotes the actual denomination written on the coins

{| class="wikitable" style="font-size: 100%;"
! Rupee              !!       Anna        !!      Pice       !!     Pie
! Paisa/Naya paisa
|-
|-
|    {{frac|192}}    || '''{{frac|12}}''' ||    {{frac|3}}    ||        '''1 pie'''
| {{frac|25|48}} ≈ 0.5208
|-
|-
|    {{frac|128}}    ||    {{frac|8}}     || '''{{frac|2}} pice''' ||    {{frac|1|1|2}}
| {{Frac|25|32}} = 0.78125
|-
|-
|    {{frac|64}}     ||    {{frac|4}}     ||      '''1 pice'''     || 3
| {{frac|1|9|16}} = 1.5625
|-
|-
|    {{frac|32}}     || '''{{frac|2}} anna'''  ||         2        || 6
| {{frac|3|1|8}} = 3.125
|-
|-
|    {{frac|16}}     ||     '''1 anna'''       ||         4        || 12
| {{frac|6|1|4}} = 6.25
|-
|-
|    {{frac|8}}      ||     '''2 annas'''       ||         8        || 24
| {{frac|12|1|2}} = 12.5
|-
|-
| '''{{frac|4}} rupee'''   ||     '''4 annas'''       ||        16        || 48
| 25
|-
|-
| '''{{frac|2}} rupee'''   ||     '''8 annas'''       ||        32        || 96
| 50
|-
|-
|      '''1 rupee'''       ||       16          ||        64        || 192
| 100
|}

[[Union of Burma|Burma]] (now [[Myanmar]]) decimalised in 1952 (predating the Indian case) by changing from the [[Burmese rupee|rupee]] (worth 16 pe, each of 4 pyas) to the [[Myanmar kyat|kyat]] (worth 100 pyas).

[[British Ceylon|Ceylon]] (now [[Sri Lanka]]) decimalised in 1869, dividing the [[Sri Lankan rupee|rupee]] into one hundred cents.

===Mauritania and Madagascar===
[[Mauritania]] and [[Madagascar]] theoretically retain currencies with units whose values are in the ratio five to one: the [[Mauritanian ouguiya]] (MRU) is equivalent to five [[khoums]], and the [[Malagasy ariary]] (MGA) to five [[iraimbilanja]].

In practice, however, the value of each of these two larger units is very small: as of 2021, the MRU is traded against the [[euro]] at about 44:1, and the MGA at about 4,600:1. In each of these countries, the smaller denomination is no longer used, although in Mauritania there is still a "one-fifth ouguiya" coin.

== Non-currency cases ==

=== Securities ===
In the special context of quoting the prices of stocks, traded almost always in blocks of 100 or more [[Share (finance)|share]]s and usually in blocks of many thousands, stock exchanges in the United States used eighths or sixteenths of dollars, until converting to decimals between September 2000 and April 2001.<ref>{{cite web|url=https://www.sec.gov/news/testimony/ts092000.htm|title=SEC Testimony: Decimal Pricing in the Securities and Options Markets (A. Levitt)|work=sec.gov}}</ref>

Similarly, in the United Kingdom, the prices of government securities continued to be quoted in multiples of {{frac|32}} of a pound ({{frac|7|1|2}}&nbsp;d or {{frac|3|1|8}}&nbsp;p) long after the currency was decimalised.

===Metrication===
{{main|Metrication}}
The idea of measurement and currency systems where units are related by factors of ten was suggested by [[Simon Stevin]] who in 1585 first advocated the use of decimal numbers for everyday purposes.<ref>{{cite web |url=http://www.britannica.com/EBchecked/topic/565994/Simon-Stevin |title=Simon Stevin (Dutch mathematician) - Britannica Online Encyclopedia |publisher=Britannica.com |access-date=2018-10-26}}</ref> The [[Metric system]] was developed in France in the 1790s as part of the reforms introduced during the [[French Revolution]]. Its adoption was gradual, both within France and in other countries, but its use is nearly universal today. One aspect of measurement decimalisation was the introduction of [[metric prefix]]es to derive bigger and smaller sizes from base unit names. Examples include ''kilo'' for 1000, ''hecto'' for 100, ''centi'' for 1/100 and ''milli'' for 1/1000. The list of metric prefixes has expanded in modern times to encompass a wider range of measurements.

While the common [[units of time]], minute, hour, day, month and year, are not decimalised, there have been proposals for [[decimal time|decimalisation of the time of day]] and [[decimal calendar]] systems. Astronomers use a decimalised [[Julian day number]] to record and predict events. Decades, centuries, and [[millennia]] are examples of common units of time that are decimalised.<ref>{{Cite book |last=Treese |first=Steven A. |url=https://books.google.com/books?id=bi1bDwAAQBAJ&pg=PA813 |title=History and Measurement of the Base and Derived Units |date=2018-05-17 |publisher=Springer |isbn=978-3-319-77577-7 |language=en}}</ref> The [[millisecond]] is a decimalised unit of time equivalent to a thousandth of a second, and is sometimes used in computing contexts.<ref>{{Cite web |title=What is millisecond? |url=https://whatis.techtarget.com/definition/millisecond |access-date=2021-10-11 |website=WhatIs.com |language=en}}</ref><ref>{{Cite web |title=What is a Millisecond (ms or msec)? - Definition from Techopedia |url=http://www.techopedia.com/definition/2730/millisecond-ms-or-msec |access-date=2021-10-11 |website=Techopedia.com |language=en}}</ref>

The [[gradian]] or grade is an [[angular unit]] defined as one hundredth of the [[right angle]] (approximately 0.0157&nbsp;[[radian|rad]]), further divided into one hundred centigrades.

In computer science, there are several metric prefixes used with [[units of information]]. For example, a [[kilobit]] is equivalent to 1,000 [[bit]]s.<ref>{{Cite web |title=Definitions of the SI units: The binary prefixes |url=https://physics.nist.gov/cuu/Units/binary.html |access-date=2022-09-20 |website=physics.nist.gov}}</ref>

=== Abbreviations for large amounts of money ===
Decimal abbreviations are sometimes used for large amounts of money. For example, the letter K (standing for [[kilo-]]) can be used to indicate that a sum of money ought to be multiplied by 1,000 i.e. $250k means $250,000. The letters M or MM can be used to indicate that a sum of money should be multiplied by a million i.e. $3.5M means $3,500,000. The letter B similarly stands for a billion.<ref>{{Cite web |author=<!--Staff Writer--> |date=2015-08-04 |title=What Does K Mean in Money? |url=https://www.reference.com/business-finance/k-mean-money-498ebfaace06af |access-date=2022-09-20 |website=Reference.com |language=en-US}}</ref><ref>{{Cite web |date=2021-07-06 |title=Billion Abbreviation: How to Abbreviate Billion |url=https://capitalizemytitle.com/how-to-abbreviate-billion/ |access-date=2022-09-20 |website=Capitalize My Title |language=en-US}}</ref>

== See also ==
* [[British coinage]]
* [[Decimal Day]]
* [[Metrication]]
* [[Non-decimal currencies]]

== References ==
{{reflist|30em}}

== External links ==
* {{cite EB9 |wstitle= Decimal Coinage |volume= VII |pages=20-21 |short=1}}

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