A dollar can be divided up into 100 cents.
A Swiss franc can be divided into 100 rappen.
What are the words that describe these units (dollar vs cents or franc vs rappen)? I found out that currencies that are based on the decimal system are called "decimalised" currencies. But I did not find a word to describe the "base unit" and the "sub unit" for arbitrary currencies.
Usage example: "This number describes <x>, but it needs to be converted to <y>".
The smaller currency unit or value, in countries that have one, is generically called a fractional monetary unit:
a monetary unit that is valued at a fraction (usually one hundredth) of the basic monetary unit
The link from Free Dictionary gives both the definition and several examples (like cent, centavo, fil, piaster). The definition also suggests that the basic unit is called just that, the basic monetary unit.
In your example, I would write:
This number describes a fractional (monetary) unit, but it needs to be converted to the basic (monetary) unit.
If you've already established you are talking about money, you can drop the "monetary," otherwise leave it as is.
The widely accepted term is minor currency unit. Also often referred to as sub-currency, minor unit or subunit.
The internationally recognized nomenclature and technical descriptions of currencies, are codified in the International Organization for Standardization (ISO) standard ISO_4217.
At the above link you will find a tabulation of the currencies of the world, with a column to indicate how many digits (if any) are after the decimal separator.
There you will see that among the most commonly exchanged currencies, EUR, USD, GBP etc have 2 digits after the decimal separator. This is probably what you refer to as decimalised, although that term (in the context of world currencies ) is probably more associated with historical transitions, most recently the change from the more arcane LSD system to decimal pennies in 1971, ref Decimal_Day. JPY is most commonly exchanged currency having no digits after the decimal separator. So Japan is an example of a country whose currency has no minor currency unit.
For your usage example, if your original wording was of the format : "This number describes cents, but it needs to be converted to dollars", it would be possible to rephrase as say : "This number describes cents which are dollar minor currency units, but it needs to be converted to dollars", but that is surely less clear that your original, to any person even minimally conversant with US currency.
If your context is indeed US dollars, the first version above will IMO, be more easily comprehensible, because the US$ is the most well known currency on the planet. On the other hand, if your context is say a travelogue and you are in a more exotic currency, it might indeed be clearer to say something like : "This number describes fils, but it needs to be converted to Dinar (given that the fils is the minor currency unit of the Iraqi dinar, such that 1 dinar is subdivided into 1,000 fils)".
From a historical point of view, the answer (considering that @DAE wants a one-word answer) is "reduction".
See the 1842 Ray's Eclectic Arithmetic 16th edition
The section on "Federal Money" starts on page 53.
First it is explained:
10 mills = 1 cent
10 cents = 1 dime
10 dimes = 1 dollar
10 dollars = 1 eagle
Then on page 56 a section "Reduction of Federal Money" begins.
Changing a number from a denomination of greater value, to one of less value, is called Reduction Descending.
Changing a number from a denomination of less value, to one of greater value, is called Reduction Ascending
Numerous books follow this terminology.
The word you're looking for is subdivision (MW)
one of the parts into which something is divided
Some example sentences:
Dollars are subdivided into cents.
Euros are subdivided into cents.
The subdivision for the Dominican Peso is centavos; 1 peso = 100 centavos.
Before decimalization, the British pound was subdivided into shillings, and then further subdivided into pence.
