4000 in roman numerals please

Reply Tue 28 Jun, 2005 08:05 am
i apologize if this has been asked before but i saw this question asked in another forum . i googled the ques and received the answer as MMMM , but this wasn't accepted by the forum ..............
Reason 1..... The RULE in Roman Numerals is that you cannot use more than three of the same symbol together.
Hence 3 is III but 4 is IV, not IIII.
And 9 is IX, not VIIII.
40 is XL, not XXXX.
90 is XC, not LXXXX.
400 is CD, not CCCC.
900 is CM, not DCCCC.
Reason 2.........4000 = IV (with a single bar across the top).
A bar on the top, and none on the bottom, multiplies the number by a thousand
Reason 3.......4000 in Roman Numerals is M followed by "V" with a line over the top.
what is it please gurus ???
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Reply Tue 28 Jun, 2005 08:15 am
4000 in roman numerals: MMMCMXCIXI

3,999 plus 1

I chose the simplist answer because my keyboard won't provide a bar to go over a V. Smile

Reply Tue 28 Jun, 2005 08:58 am
According to this, the Romans placed a bar above a numeral to represent 1000 times that value. So 5000 is Vbar. Using that nomenclature 4000 would be MVbar or IbarVbar.

0 Replies
g day
Reply Sun 17 Jul, 2005 11:33 pm
MMMM or (IV ) bar - depending on when in time the question was asked. If you were asked how would this be written 3,000 years ago - answer would be MMMM, if your time frame was only 1,500 years either answer would suffice - Romans weren't too good on the standards with numbering.

The key rules to remember are:

1. always express a number the simplest way possible - so long as it complies with the further rules:

2. digits 2, 3, 6, 7, 8 are always expressed as additive, digits 4 and 9 are always subtractive

3. subtractive rules:

I can only be subtracted from V or X,
V subtracts from nothing per rule 1,
X can only be subtracted from L or C,
L subtracts from nothing - per rule 1,
C subtracts only from D or M,
D subtracts from nothing per rule 1 too!

4. A bar under a numeral multiplies it by 1000 (from about 1000 AD this rule was invented). I guess double bar multiplies by 1,000,000

5. There is no zero (that was invented around 1500 AD - the romans were all gone by then Smile )

6. Larger numbers always come before smaller numbers, unless a valid subtractive rule (i.e. 4 or 9) are being applied

* * *


800 is DCCC, never CCM (rule 2), or DMCCC (rule 1)

1000 is M not DD or CMC (rule 1) or XMX (rules 1 and 3)

999 is CMXCIX, not IM (rule 3) or XMIX (rules 1 and 3)

44 is XLIV, not XXXXIV or XXXXIIII or VIL (rules 1, 2 and 3)

15 is XV, never XVX (per rules 1 and 3)

VIX or IVX (meaning possibly V(IX) or (VI)X and I(VX) or (IV)X) are all illegal per rule 6!

4,000 is MMMM or (IV ) bar - depending on when in time the question was asked. If you were asked how would this be written 3,000 years ago - answer would be MMMM, if your time frame was only 1,500 years either answer would suffice - Romans weren't too good on the standards with numbering.
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Reply Tue 22 Apr, 2008 08:46 pm
g__day: I agree in part with what you say but I actually think the rules are simpler. I would propose something like this:

1. Never use more than 3 instances of a symbol.
Since we have a new symbol for each 5 numbers, this means that we will subtract all numbers in the form 5x-1 (that is, 4,9,14,19,40,90, etc)

2. The number to be subtracted is always equivalent of a single unit in the current position (tens, hundreds, etc) or in the position immediately before. this means that we'll have IV (same position) and IX (immediately before), XL and XC, but never IC or XM

3. A bar over (or below) a symbol multiplies its value by 1,000. Double bar multiplies it by 1,000,000.

With this set of rules, MMMM is discarded per rule 1., and IV is not allowed per rule 2.

Note that we may get tempted to use IV since V (which is the correct form of 5,000) resembles V, and actually is based on the same symbol -- but it is *not*. It is a totally new symbol, and we should treat it as such.

That said, 4,000 would be represented, IMO, as MV. then V, VM, VMM, VMMM and MX. This is the form that complies with the rules used for all the numbers below.

In an attempt to illustrate the concept, look below for example:

Note how each line keeps using the same letter for a single unit (I,X,C,M) and compare to the last line showing the alternative, treating the V as a regular V (and thus being preceded by Is instead of Ms, breaking the symmetry of the line)

I hope I could make my point clear, at last: 4,000 = MV.
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Reply Tue 22 Apr, 2008 09:23 pm
Very clear, waldir, just a tad late.
Fingers asked the question in 2005 Smile

Great explanation though, and welcome to a2k!
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Reply Tue 22 Apr, 2008 09:39 pm
Hi CalamityJane, thanks for the welcoming!

Lol I knew I'd be late so I didn't even look at the dates Razz

I was asked earlier today to make a small program to convert decimal numbers into roman numerals, with the upper limit of 3999. I decided to go further and implement more numbers. Currently it supports numbers up to 999,999,999 (I could add more with a triple overline, but I thought it would start getting too cluttered), the script can be found in http://waldir.awardspace.com/other/Dec2RomExtended.html

However, I fell for the fallacy I described in my previous post, using Is for numbers like 4000 and up. I got a little confused while testing the script, and started to research on the net to see if I could find a clarification on the issue. This page was one of the most useful ones out of the several dozens I found, and I decided to post my conclusions here to add to the excellent thoughts that have been shared here.

I am now in the process of rewriting my code, it should be uploaded soon with the correct behavior. By the way, I incidentally found that there are apparently no online converters that accept numbers above 9,999; and those that accept 4,000+ use nonstandard multiple Ms (up to MMMMMMMMM for 9,000). So I hope my converter can add some value and innovation to the web Very Happy

PS-sorry for the long post...
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Reply Tue 22 Apr, 2008 10:02 pm
That sounds very interesting, waldir, and yes, such a converter could
be very helpful, especially to those who have not been taught Roman
numbers previously.

Thank you!
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Reply Tue 22 Apr, 2008 10:09 pm
Years ago, I learned from the World Almanac that a bar over the letter is multiplication by 1000.

Not that wikipedia is always correct, but they show 4000 as IV with a bar on top.
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Reply Tue 22 Apr, 2008 10:21 pm
markr, look at the history of the article (I assume you're talking about "Roman numerals", right?)

Yes, it was actually me who edited it Razz, while I was starting my research, since it was using MMMM for 4,000, but VI, etc for the following thousand values and at the time I was still under a fallacy as I described in my previous post.

I now reached a conclusion, which I posted above, and I will soon edit the articles ("Roman numerals", "4000 (number)", and others) accordingly.

Never forget that Wikipedia is always a work in progress Wink
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Reply Wed 23 Apr, 2008 01:29 am
That page is changing often! Your mod has already been undone and redone.

Out of curiosity, how did you arrive at your conclusion, and how is it conclusive? There seem to be differences of opinion out there.
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Reply Wed 23 Apr, 2008 07:41 am
Oh, as I said, that's just my opinion. I am aware that there are several different opinions out there. But, I dare saying, almost none of them are properly justified without relying on tradition/historical use (as opposed to the logic of the system).

My "conclusion" was thus based on logic purely, trying to follow the patterns of the previous numbers.

Firstly, I discarded MMMM as in no other previous number four instances of the same symbols appear. The roman system has somewhat of a mixed base (base 10 with the pseudo half-base 5), and the number immediately before a base/half-base is always subtracted. This happens at all levels, be it units, tens (base^2), hundreds (base^3), etc.

Second, I discarded IV since all subtractions occur with the "unit" symbol of the same level (like XL, CD), or of the level immediately before (like IX, CM). The "unit" symbol of the V level (which is tens of thousands) is M, not I. Actually, I is never used except is the (strictly speaking) units level.

In fact, you would see that most instances that use V instead of multiple Ms (that is, those who tried a more serious approach) used VM, VMM, etc; instead of VI and so on. I guess people haven't spent too muck time thinking of it.

Using a I-bar here goes not only against the previous-level approach. It breaks a wide set of logic rules:
- Never before two new symbols are introduced at once; this only happens one by one, in groups of base^n (using the base 10 and its pseudo half-base 5, this translates to 5, 10, 50, 100, etc) numbers
- It breaks the simplicity rule. If we already have a symbol for M, it doesn't make sense to use I, which is equivalent and adds ambiguity to the system. Each different symbol should have its own value. Duplicates are obviously a bad approach.

Now, I realise that this strict set of rules didn't exist in this exact formulation in the Romans' time. They were flexible enough to use IIII instead of IV several times (but not VIIII instead of IX, I must point out -- one more inconsistency).

So these rules may not be canon, may not be tradition. But we must remember that they didn't need to represent very big numbers often. If we truly want the system to be consistent and (more importantly) scalable, we have to stick to a set of simple common rules, instead of relying in exceptions which are in use as legacy/tradition only; not because they make sense.

PS - I do find it a pity that we can't have all thousands overlined/underlined, which would be a much easier way to read the symbols: for instance, 8,034 would be VIIIXXXIV instead of the ugly and less intuitive VMMMXXXIV. But then, for consistency, we'd have to discard the M, having 2008 represented as IIVIII instead of the canon MMVIII. This was also something I tried to follow in my reasoning: relying on the current standards of use as much as possible, as long as they are widespread enough, that is.

A good solution would be having a different letter for 5,000. That way, most problems would be solved -- but we would still have the overline/underline only in the tens of thousands, which contradicts with our sense of using group separators for thousands. We logically expect both that the underline/overline covers the whole thousands section instead of just part of it; and we wouldn't read XMVC it as fast as XIVC.

A workaround to this could be using I instead of M everytime a number greater than 3999 is used. It would make more sense to the reader (actually it is what I implemented on my converter, before I reached the conclusion that it was wrong), but would break the rules of simplicity as I stated above (and the symmetry, as I showed in my first post on this thread)

Actually, the only solution that would work would be dropping the M and using I exclusively, as I stated above. So, given all this, do you agree that MV is the correct way? Or would you choose dropping the Ms? Note the latter has been used historically, see for instance some examples here, so there definitely would be some historical background to back us up. Actually, that link supports a theory that M is actually an evolution of the (I) form, which was a common way to represent thousands. This means that I is even more canon than M! Razz So, what do you think of all this?
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Reply Thu 24 Apr, 2008 12:04 am
I think it should be documented the way it was used (perhaps that varied over time - I haven't done any research) and not the way we think it should be. So, for documentation purposes, I'd go with the traditional/historical use instead of the (perhaps determined after the fact) logic of the system.

Having said that, if it were to be (re)defined today to make it more logical/consistent, I wouldn't have a multiplier that equals one of the symbols. I'd either drop M and multiply by 1000, or add a symbol for 5000 and multiply by 10000. I wouldn't feel the need to make the multiplier 1000 to match the modern grouping convention because it differs so much anyway.
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Reply Thu 24 Apr, 2008 12:28 am
Thanks for your thoughts. As you said, for documentation purposes, the traditional uses should be followed rather than the logical ones. The problem with this approach is that several methods have been used over time. Should we use the most ancient ones? the most widespread ones? should we consider modern day usage as widespread, or restrict to a specific time frame (the duration of the roman empire for instance -- IF it has precise dates for start and end, that is). Lots of questions arise, but I'll leave that research to someone else.

What I am interested is in the mathematical side of the system: for conversion purposes, we have to have a simple and consistent set of rules and as little exceptions as possible. I'm considering 4s and 9s as exceptions, for instance.

I found what you said very logical and clear: It doesn't make sense to have a multiplier that equals one of the symbols. From the two options you present, I'd choose dropping M for 2 reasons:

* We wouldn't have to come up with a new symbol. This would probably be reinventing the system a bit too much. I, on the other hand, is an existent symbol, with historical background -- perhaps even a more solid one than M, as I noted above.

* We don't have to make the multiplier match the modern grouping convention, but given the choice, why making it harder? In any case, using 1,000 as a multiplier once more has historical background, while 10,000 doesn't. So again, we'd be reinventing the system -- in fact we'd be clashing with it, since the multiplier symbol would mean something different than it did in the past.

I must thank you for helping me get my thoughts clear. It is now evident to me that the most logical system (while complying to the canon rules and traditions as much as possible) is indeed dropping the M symbol completely and replacing it with I. I will update my converter accordingly, and link to this discussion as an explanation.
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g day
Reply Mon 28 Apr, 2008 01:03 am
Initially it would have been written IIIIIIIII...I, so you have to include time frame when you ask your question.

Too the no more than three in a row fails past the thousand, because for example Millions by convention can be M bar or a string of Ms - depending on the timeframe the question was asked in - both where valid in their time. I don't think they would have ever written a super complex construction to avoid more than three - they just weren't that focused on really big (to them) numbers!
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Reply Mon 28 Apr, 2008 01:37 pm
Hey g__day, thanks for your thoughts, and welcome back to the discussion! Very Happy It's been a while, huh? Wink
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rhaiza cutie
Reply Wed 16 Jun, 2010 07:22 am
my question is ,what will you do if the roman number has a barline on the top of it????pls answer this question
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Pamela Rosa
Reply Mon 25 Jul, 2011 06:47 am
fingers47 wrote:

Hence 3 is III but 4 is IV, not IIII.


4000 in roman numerals: MMMM
0 Replies
Pamela Rosa
Reply Mon 25 Jul, 2011 07:15 am

|XL| = 40 * 100 = 4000 (instead of MMMM)
Reply Mon 19 Oct, 2015 05:19 am
@Pamela Rosa,
Nope, || doesn't mean x100. ___ means x1000. There is no such thing to say x100 in the Roman numeral notation. So 4000 is either MMMM (in Addition, subtraction, multiplication and division for the Roman numeral notation),
IV (Not so many used but kind of correct) and
MV (Absolutely correct)
Also I Amman the one who entered University in the age of 8 and now I am almost graduated.
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