What a Roman Legionary needs to know in order to count in Ancient Rome

Study Well  -  There may be a Test !

Roman Numerals was the standard numbering system and method of Arithmetic in Ancient Rome and Europe until about 900 AD,  when the Arabic Numbering System, which was originated by the Hindu's,  came into use.   The concept of  "Zero"  did not exist in Europe until after 1000AD;  thus, there was no roman numeral symbol for "Zero".   If you think adding or subtracting in roman numerals is clumsy;  try multiplication or - "horrors"- long division!   Only seven numeral-characters were used and when a numeral was over-lined,  it represented the base-value,   multiplied by a thousand.    This convention is really no longer used,  as roman numerals are seldom utilized for values beyond 4999.   It is shown here for demonstration only.    Due to the difficulty of representing an over-line with a computer font,   an under-line has been substituted.   In some styles of Roman Numerals,   "D" is sometimes represented by an "I" followed by a backwards "C", something like "I)";  and "M" is shown as a "C" followed by an "I" and a backwards "C".    Likewise,  this form is not possible with standard computer fonts;   and therefore,  is not utilized here.

        I = 1        V = 5               X = 10               L = 50               C = 100               D = 500             M = 1000

                        V = 5,000        X = 10,000        L = 50,000        C = 100,000        D = 500,000      M = 1,000,000

Placing an "I" in front of the "V";  or placing any smaller value in front of any larger value,  indicates subtraction.  That is,   the preceding smaller value is subtracted from the following larger value.  So "IV" means 4.  The value "IIII" is sometimes used for "4".  "IIII" is used mostly on faces of clocks and for other special uses.  The standard Roman Numeral for "4" is  IV.

The subtractive principle for Roman numbers does have some restrictions 

You can only subtract a power of ten, and only from the next two higher "digits", where the digits are  either I, V, X, L, C, D, M.
I.E. - Only I, X and C can be subtracted, AND  I  can only be subtracted from V and X; X can only be subtracted from L and C; C can only be subtracted from D and M.
Using these limits of subtraction, the Roman numerals IL for instance, for 49 and IC for 99 are not valid. 
The correct representation for 49 is XLIX, and 99 is XCIX.

Placing a smaller value after a larger one indicates that the smaller value is added to the preceding larger value.  Thus,  after V comes a series of additions - VI means 6, VII means 7, VIII means 8.

ARABIC                      C A R D I N A L                      O R D I N A L    LATIN
      one - two - three - four - etc ....1...2...3...4...5...6...7...8...9...10...etc first - second - third - fourth - fifth - 1st - 2nd - 3rd - 4th - 5th - 6th - etc  
             1 unus - una - unum primus           I
             2 duo - duae - duo secundus          II
             3 tres - tria tertius         III
             4 quattuor quartus        IIII 
             5 quinque quintus         V
             6 sex sextus         VI
             7 septem septimus        VII
             8  octo octavus       VIII
             9 novem nonus         IX
           10 decum decimus          X
           11 undecim undecimus         XI
           12 duodecim duodecimus        XII
           13 tredecim tertius decimus       XIII
           14  quattourdecim quartus decimus       XIV
           15 quindecim quintus decimus        XV
           16 sedecim sextus decimus       XVI
           17 septendecim septimus decimus       XVII
           18 duodeviginti duodevicesimus       XVIII
           19 undeviginti undevicesimus       XIX
           20 viginti vicesimus        XX
           21 viginti unus vicesimus primus       XXI
           22 viginti duo  -  duo et viginti   (2 & 20) vicesimus secundas       XXII
           23 viginti tria  -  tria et viginti     (3 & 20) vicesimus tertius       XXIII
           24 vicesimus quartus       XXIV
           30 triginta tricesimus       XXX
           40 quadraginta quadragesimus        XL
           48 quadraquattoroctem quadraquatttoroctavus      XLVIII
           49 quadraquattornovem quadraquatttornovus        XLIX
           50 quinquaginta quinquagesimus          L
           60 sexaginta sexagesimus        LX
           70 septuaginta septuagesimus        LXX
           80 octoginta octogesimus       LXXX
           90 nonaginta nonagesimus         XC
           98 nonagintaoctem nonagintaoctavus       XCVIII
           99 nonagintanovem nonagintanovus        XCIX
         100 centum centesimus          C
         101 centum unus  -  centum et unus  (100 & 1). centesimus primus          CI
         102 centesimus secundas          CII
         200 ducenti,  -ia,  -a ducentesimus          CC
         300 trecenti trecentesimus          CCC
         400 quadringenti quadringentesimus          CD
         500 quingenti quingentesimus            D
         600 sescengenti sescentesimus           DC
         700 septingenti septingentesimus          DCC
         753 sepingenti quinquaginta tria Year of Rome's Founding    -                     April 21, 753 BC     DCCLIII
         800 octingenti octingentesimus     DCCC
         900 nongenti nongentesimus         CM
       1000 mille millesimus           M
       1001 mille unus millesimus primus           MI
       1002 mille duo millesimus secundas          MII
       1003 mille tre millesimus tertius         MIII
       1900 mille nongenti millesnongentesimus       MCM
       1999 mille nongenti nonginta novem Year of Current Era MCMXCIX
       2000 duomilia bismillesimus                                               Last year of 20th Century         MM
       2001 duomilia unus bismillesimus primus                                     1st Year of 21st Century         MMI
       2002 duomilia duo bismillesimus secundas        MMII
       2003 duomilia tre bismillesimus tertius      MMIII
       2004 duomilia quattuor bismillesimus quartus      MMIV
       2100 duomilia centum bismilles centesimus        MMC
       2752 duomilia sepingenti quinquaginta duo  "AUC" Year of  Ancient Rome   -                              Ab Urbe Condita MMDCCLII
       3000 tresmilia tresmillesimus       MMM
       4000 quadramilia quadramillesimus    MMMM
       5000 quinmilia quinmillesimus            V
       6000 sesmilia sesmillesimus           VM
       7000 septuamilia septuamillesimus         VMM
       8000 octomilia octomillesimus      VMMM
       9000 nonamilia nonamillesimus          MX
    10,000 decem milia decies millesimus            X
    10,001 decem milia unus decies millesimus primus            XI
    10,010 decem milia decem decies millesimus decimus           XX
    11,000 undecim milia undecim millesimus           XM
    12,000 duodecim milia duadecim millesimus         XMM
    12,100 duodecim milia centum        "            "      centum       XMMC
    12,505 duodecim milia quingenti quinque     "     "  quingenti quinque    XMMDV
    50,000 quinqua milia quinqua millesimus             L
    50,100 quinqua milia centum quinqua millesimus centum            LC
    50,500 quinqua milia quingenti quinqua illesimus quingenti            LD
    60,000 sexa milia sexa millesimus           LX
    60,010 sexa milia decem sexa millesimus decem          LMX
    60,100 sexa milia centum sexa millesimus centum          LMC
    80,004 octo milia quarttuor octo millesimus quartus   LMMMIV
   90,099 nona milis novaginta novem nona millesimus nonus    MCXCIX
  100,000 centum milia centies millesimus             C
  100,001 centum milia unus centum millesimus primus            CI
  100,010 centum milia decem centum millesimus decem           CX
  200,000 ducenta milia ducenta millesimus           CC
  200,100 ducenta milia centum ducenta millesimus centum         CCC
  200,510 ducenta milia quindecem      "          "     quindecem      CCDX
  500,000 quingenti milia quingenti millesimus            D
  600,000 sescenti milia sescenti millesimus          DC
  600,606 sescenti milia sescenti sex      "         "    sescenti sex   DCDCVI
  700,000 sepusducenta milia sepcenti millesimus          DCC
1,000,000 mille milia mille millesimus            M
1,100,100 mille milia centum milia centum "    "  centum miliacentum          MCC
1,300,000 mille milia trecenti mille "    "   trecenti mille       MCCC
2,000,000 duamilia milia duamilia millesimus          MM
2,500,500 duamilia milia quingenti milia quingenti " " quingenti milia quingenti       MMDD
      You Saw It Here First !?

When a numeral has an underline or an overline,  its value is increased a thousandfold.

  X (10,000)  =  X (10)  times  1000    ***   C (100,000)  =  C (100)  times   1000  

Roman numerals was the standard, and as far as we know,  the only number system used by the Romans and other  ancient Europeans.  Roman numerals were used primarily for counting,  as the ancients had little use for,  or understanding of  "calculation" or arithmetic as we know it today.   With some effort, you can do regular addition and subtraction and even multiplication with Roman Numerals;  as both the Roman Numeral and later Arabic Number systems are both "base-10" (1 thru 9).   Zero came later.    Long division?  Well that would be a chore,  more like calculation.

Without a concept for the value of "zero" or "nothing",  accurate calculation or mathematics with Roman Numerals would be flawed and near impossible.   But; for the basic arithmetic in use in ancient times,  this apparently was not that big a problem, and of course,  they did not realize they had the "zero" problem in the first place.

See  Why No Year Zero  for more on "Zero".

Early electronic computers used a "base-8" or "octal" (0 thru 7) number system and today's computers use "base-16" or "hexadecimal" notation (0 thru 15 or 0 thru F ) with "A thru F" representing the numbers "10 thru 15" respectively. 

That is,   6 + 4 = A(10)   7 + 5 = C(12)   7 + 8 = F(15)   8 + 8 = 10(16, 1 x 16 +0)   A(10) + A(10) = 14(20, 1 x 16 +4)  in "Hexidecimal";  thus:  decimal 32 = hex 20(2 x 16 + 0)   and  decimal 64 = hex 40(4 x 16 + 0) .    

The rules for counting and arithmetic are the same.  You just have to remember when to "carry-over" to the next value level,  8 or 10 or 16.

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