# Short or long Roman numerals?

TL;DR: Is 1995 correctly written as MVM, or as something more like MCMLVL? MCMVC? MCMLXLV? MCMLXXXXV?

From what I recall from my Latin classes (European highschool...), you are not supposed to write more than 3 identical subsequent symbols. However, this rule hasn't been consistently followed in modern times from what I can tell by a little web research.

Perhaps it'd help if I knew how the Romans themselves wrote larger numerals... Would they write CLXL or CXC for 190? Something else still?

1995 = MCMXCV.

The rules are:

first triad: I, V, and X:
I, II, III, IV, V, VI, VII, VIII, IX, X

Then all is repeated with:
second triad: X, L, and C
third triad: C, D, and M

You can't use letters outside of their "triad": So, IM for 999 is wrong. CXC for 190 is correct, and 195 is CXCV (not CVC).

You should write numbers in decreasing order: thousands first, then hundreds, then tens, and finally the ones.

There exists even more ancient (wiki) "Longer scheme" (Even now it is sometimes used for clocks):
I, II, III, IIII, V, VI, VII, VIII, VIIII, X... If you use it, you must use it for all three triads, of course.

• was it really widespread in ancient times, or is it a modern mistake?
– o0'.
Commented Feb 6, 2012 at 15:17
• It is the older form. Previously Romans used it and only it. Later changed to the other one. I don't remember when. But I have met this longer form sometimes in real life. I don't remember exactly, Maybe on cemetry. But now I think, there it could be an error... Commented Feb 6, 2012 at 15:22
• Looks very strange to me, I'd ask for a authoritative source here...
– o0'.
Commented Feb 6, 2012 at 15:24
• en.wikipedia.org/wiki/Roman_numerals - look clocks there. Commented Feb 6, 2012 at 15:29
• Oh! I was right - these VIII and even IIII forms ARE more ancient! The answer edited again. Commented Jun 20, 2013 at 15:00

The Roman numeral system was "designed" for calculating using an abacus.

One wrote out the number by the values of each channel (we picture an abacus as a wood frame with wires holding columns of beads for counters but the Romans would usually have used a table, a "TV-tray" if you will, covered with ample sand, running a finger down for the lines, and placing small stones in the channels for the counters).

The use of "fives" (i.e.: one counter for half a column's value) cut down on moving counters. Nothing to do with the Etruscans as we are always told. Each "five" (half column value) symbol was literally the column's symbol cut in half. "V" = top half of "X" and so on, though long before the realization their symbols for numbers mostly matched various letter symbols (mid-100's BC).

One did not only write out the results going column by column, one read them in to establish the first value, then to work in the other values in the calculation.

So chunk by chunk, if you will. "MVM" would never have been done because the "V" literally had nothing to do with the "M" and "C" columns. One had individual hundreds of half the column (500) to subtract from the "M" but the "V" column (the tens) only affected the "C" (hundreds column), not a second or fifth or whatever column further left.

Hence 1995 moves one "M" counter ("M" of "MCMXCV"), then the half and 4 "C" counters (physically: move the half counter, then all the single hundred counters (the "M" in "CM"), then move one back up ("subtract" it - the "C" before the "M" in "CM"), then the same process with the "XC" (tens column) as just done for the hundreds channel, and finally, move the half in the ones column.

(Note that just a bit of that is notional. They used 4 counters in the bottom of the abacus, not 5, so one pretended to be moving 5 down, then one back up. This is why I was a little cagey expressing it above.)

Again, the "V" would NEVER come before the "M" except when one wished to be... less traditional... whimsical... that kind of thing. It would aggravate most users. Picture some modern Japanese abacus expert challenging Western calculator users having his skilled, efficient, magic fingers jammed up by reading the Japanese equivalent of "MVM" - he'd be crying foul pretty quickly.

Although... the Romans were just as we are. They even dropped numbers into words to shorten the writing of them, much like a 12yo texting friends.

Roman numbers maintained for so long because the underlying technology for calculation had to have an alternative and the uses to which they were put had to form a need. It is no surprise that Hindu numbering did not come into heavy enough usage to replace Roman number use until bookkeeping moved into the ledger phase in which columnar presentation which required simpler representation of values to work well. Picture what a ledger, or spreadsheet for that matter, would look like if each column were broken into "digit" columns (those green ledger books everyone has seen) in which an entry might read "C" or "DCCC" vs. the Hindu single digit "1" or "8": far more compact and "regular" and hence far easier to grasp at a glance.

Handling the Hindu numbers had been figured out 700-1,500 years earlier depending on which "evidence" one accepts. But it required a surface like an elephant leaf to write upon, or paper. Paper it turns out was amenable to industrial scaling and so became cheap enough to use for mundane things.

The last portions somewhat exceed the bounds of the question in content, but I included them to emphasize the importance of utility in most things man does. Roman numerals were the product of the sole good method of calculation that existed for a very long time. And cheap: one just removed his counters, smoothed the sand, drew his columns, and everything was fresh. Cheap, once one learned the system. Try that with paper and even pencil!

• It's worth noting that the abacus itself is a representation of the human hand, with its thumb and four fingers. I fancy a mental image of the abacus being invented by a man who didn't have 10 slaves handy with their hands held out for manipulation. Commented Sep 8, 2015 at 1:25