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 to a power of 10, most commonly 100 and exceptionally 1000; and sometimes at the same time changing the name of the currency or the conversion rate to the new currency. Today, only two countries have non-decimal currencies: Mauritania, where 1 ouguiya = 5 khoums, and Madagascar, where 1 ariary = 5 iraimbilanja. However, these are only theoretically non-decimal, as in both cases the value of the main unit is so low that the sub-units are too small to be of any practical use and coins of the 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 ruble being equal to 100 kopeks,  but it is the USA's version of decimalisation that has been adopted across most of the world, with several countries even using the same terminology of dollar and cent.
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 factors. 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 exception of the United States and, to a lesser extent, the United Kingdom. Thus a kilometre is 1000 metres, while a mile is 1,760 yards. Electrical units are decimalised worldwide. Common units of time remain undecimalised; although an attempt was made during the French revolution, this proved to be unsuccessful and was quickly abandoned.
Some countries changed the name of the base unit when they decimalised their currency, including:
|New unit||=||×||Old unit||Year|
|German gold mark||=||1/3||Vereinsthaler||1873|
|South African rand||=||½||South African pound||1961|
|Australian dollar||=||½||Australian pound||1966|
|New Zealand dollar||=||½||New Zealand pound||1967|
|Fijian dollar||=||½||Fijian pound||1969|
|Nigerian naira||=||½||Nigerian pound||1973|
Russia converted to a decimal currency under Tsar Peter the Great in 1704, with the ruble being equal to 100 kopeks, thus making the Russian ruble the world's first decimal currency, but not quite as we know decimal currencies today, as there were smaller units beneath the kopek itself, the Denga (200 of which made a ruble) and the Polushka (400 of which made a ruble). With the Russian Revolution the Soviet Union adhered to the US model by no longer subdividing the kopek.
France introduced the franc in 1795 to replace the livre tournois, abolished during the French Revolution. France introduced decimalisation in a number of countries that it invaded during the Napoleonic period.
Decimalisation in Canada was complicated by the different jurisdictions before Confederation in 1867. In 1841, the united Province of Canada's Governor General, 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. In June 1851, the Canadian legislature passed a law requiring provincial accounts to be kept decimalised as dollars and cents. The establishment of a 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". 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:
|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|
|Prince Edward Island||1871|
The colonial elite, the main advocates of decimalisation, based their case on two main arguments: 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.
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.
The 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. It replaced the South African pound as legal tender, at the rate of 2 rand = 1 pound or 10 shillings to the rand. Australia, New Zealand and Rhodesia also chose ten shillings as the base unit of their new currency.
Australia decimalised on 14 February 1966, with the Australian dollars 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. New Zealand decimalised on 10 July 1967, with the New Zealand dollars replacing the New Zealand pound.
In both countries, the conversion rate was one pound to two dollars and 10 shillings to one dollar.
|5 shillings||50 cents|
|2 shillings||20 cents|
|1 shilling||10 cents|
|6 pence||5 cents|
|3 pence||2.5 cents|
|1.2 pence||1 cent|
|1 penny||5⁄6 cent|
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 lowest common multiple of both systems) during the transition.
Yemen Arab Republic introduced coinage system of 1 North Yemeni rial=100 fils in 1974, to replace former system of 1 rial = 40 buqsha = 80 halala = 160 zalat. The country was one of the last to convert its coinage.
Japan historically had two decimalisations 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 round amounts of 1 yen or greater.
In India, Pakistan, and other places where a system of 1 rupee = 16 annas = 64 paise = 192 pies was used, the decimalisation process defines 1 naya paisa = 1⁄100 rupee. 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
|1⁄192||1⁄12||1⁄3||1||25⁄48 ? 0.5208|
|1⁄128||1⁄8||1⁄2||1+1⁄2||25⁄32 = 0.78125|
|1⁄64||1⁄4||1||3||1+9⁄16 = 1.5625|
|1⁄32||1⁄2||2||6||3+1⁄8 = 3.125|
|1⁄16||1||4||12||6+1⁄4 = 6.25|
|1⁄8||2||8||24||12+1⁄2 = 12.5|
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 to one, and the MGA at about 4,600 to one. In each of these countries, the smaller denomination is no longer used, although in Mauritania there is still a "one-fifth ouguiya" coin.
In the special context of quoting the prices of stocks, traded almost always in blocks of 100 or more shares 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.
Similarly, in the UK, the prices of government securities continued to be quoted in multiples of 1⁄32 of a pound (7+1⁄2 d or 3+1⁄8 p) long after the currency was decimalised.
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. 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 prefixes 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 decimalisation of the time of day and decimal calendar systems. Astronomers use a decimalised Julian day number to record and predict events.