Classical Roman use only allows the longer form and also requires the use of the subtractive notation for any 4 or 9 digit.
In medieval times, however, IL, IC, XD or XM were occasionally seen as shorthand, much like Church Latin omitted a few of the most complex classical Latin constructions.
The IIII occasionally seen evolved from clock making - it was created as an aesthetic counterweight to make the right hand half of the clock face seem less empty and improve symmetry.
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