This process has been undergone by most countries in Europe. France decimalised at the time of the Revolution, and imposed decimalisation on a number of countries that it invaded at that time. Many countries in the world decimalised on achieving independence from Britain, the first to do so being the United States. However some Commonwealth countries retained traditional money systems after achieving effective independence as Dominions, and decimalised more recently. For example Australia decimalised in 1966.
The United Kingdom decimalised on February 15, 1971, from its previous system of poundss, shillings, and pence to a system of units with 100 "new pence" to a pound, which kept the same value as before. As there were previously 20 shillings, each of 12 pence, in a pound, each "new penny" (or "pee", since the abbreviation p for pence replaced the old d for denarii which was used as an abbreviation for old pennies) was worth exactly 2.4 old pence, and 5 new pence were equivalent to an old shilling. 10 new pence were equivalent to a florin (a coin introduced in 1849 to facilitate a decimalisation that was expected to follow quite soon). Children found the new system easy to grasp, but many older people struggled to adapt to the new system.
When Australia decimalised, the currency was renamed the Australian dollar in the process, as the size of the basic currency unit was changed (to ten of the old shillings, i.e. half the value of the previous pound). A similar strategy was followed in New Zealand and South Africa (where the new unit was called the rand). In Britain, consideration was given to having a new "decimal pound" worth ten shillings in the old currency which would have resulted in the "decimal penny" being worth only slightly more than the old penny; in the event, it was decided that Sterling's importance as a reserve currency meant that the Pound should retain its former value.
In France, decimalisation of the coinage was accompanied by metrication of other measures. However, in general the two have not gone hand in hand: the U.S. has never metricated, Canada has only recently done so despite having long had a decimal coinage, and the U.K. has only metricated to a limited extent.