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A medieval system developed from a cruder Roman system. The system of Roman numerals is based on using special symbols to denote decimal digits <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825601.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825602.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825603.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825604.png" />, and their halves <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825605.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825606.png" />, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825607.png" />. Positive integers are written by repeating these numerals. When a letter is followed by a letter of lesser value, the values are added (addition principle), when a letter is followed by a letter of greater value, the smaller is subtracted from the larger (subtraction principle). The latter rule is only applied in order to prevent a fourfold repetition of the same letter. In this system it is rather inconvenient to carry out arithmetic operations with multi-digit numerals. At present, the Roman numerals are no longer used, except in certain cases such as the designation of centuries and years A.D. and also months when designating dates, ordinal numbers and sometimes derivatives of low order higher than three: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825608.png" />, etc.
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A medieval system developed from a cruder Roman system. The system of Roman numerals is based on using special symbols to denote decimal digits  $  I = 1 $,
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$  X = 10 $,
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$  C = 100 $,
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$  M = 1000 $,
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and their halves  $  V = 5 $,
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$  L = 50 $,
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$  D = 500 $.
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Positive integers are written by repeating these numerals. When a letter is followed by a letter of lesser value, the values are added (addition principle), when a letter is followed by a letter of greater value, the smaller is subtracted from the larger (subtraction principle). The latter rule is only applied in order to prevent a fourfold repetition of the same letter. In this system it is rather inconvenient to carry out arithmetic operations with multi-digit numerals. At present, the Roman numerals are no longer used, except in certain cases such as the designation of centuries and years A.D. and also months when designating dates, ordinal numbers and sometimes derivatives of low order higher than three:  $  y ^ {IV } , y  ^ {V} $,
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etc.
  
 
====Comments====
 
====Comments====
The cruder Roman system referred to above is as follows: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r0825609.png" /> was represented by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256010.png" /> between parenthesis: <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256011.png" />; <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256012.png" /> was represented by <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256013.png" />, etc. Later <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256014.png" /> became <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256015.png" />. Half of it, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256016.png" />, later became <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256017.png" />.
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The cruder Roman system referred to above is as follows: $  1000 $
 +
was represented by $  1 $
 +
between parenthesis: $  ( 1) $;  
 +
$  10  000 $
 +
was represented by $  (( 1)) $,  
 +
etc. Later $  ( 1) $
 +
became $  M $.  
 +
Half of it, $  {} 1) $,  
 +
later became $  D $.
  
A partial list of Roman numerals is:''''''<table border="0" cellpadding="0" cellspacing="0" style="background-color:black;"> <tr><td> <table border="0" cellspacing="1" cellpadding="4" style="background-color:black;"> <tbody> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256018.png" /></td> <td colname="2" style="background-color:white;" colspan="1">I</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256019.png" /></td> <td colname="5" style="background-color:white;" colspan="1">XXX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256020.png" /></td> <td colname="2" style="background-color:white;" colspan="1">II</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256021.png" /></td> <td colname="5" style="background-color:white;" colspan="1">XL or XXXX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256022.png" /></td> <td colname="2" style="background-color:white;" colspan="1">III</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256023.png" /></td> <td colname="5" style="background-color:white;" colspan="1">L</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256024.png" /></td> <td colname="2" style="background-color:white;" colspan="1">IV or IIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256025.png" /></td> <td colname="5" style="background-color:white;" colspan="1">LX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256026.png" /></td> <td colname="2" style="background-color:white;" colspan="1">V</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256027.png" /></td> <td colname="5" style="background-color:white;" colspan="1">LXX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256028.png" /></td> <td colname="2" style="background-color:white;" colspan="1">VI</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256029.png" /></td> <td colname="5" style="background-color:white;" colspan="1">LXXX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256030.png" /></td> <td colname="2" style="background-color:white;" colspan="1">VII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256031.png" /></td> <td colname="5" style="background-color:white;" colspan="1">XC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256032.png" /></td> <td colname="2" style="background-color:white;" colspan="1">VIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256033.png" /></td> <td colname="5" style="background-color:white;" colspan="1">XCIX or IC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256034.png" /></td> <td colname="2" style="background-color:white;" colspan="1">IX or VIIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256035.png" /></td> <td colname="5" style="background-color:white;" colspan="1">C</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256036.png" /></td> <td colname="2" style="background-color:white;" colspan="1">X</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256037.png" /></td> <td colname="5" style="background-color:white;" colspan="1">CI</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256038.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XI</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256039.png" /></td> <td colname="5" style="background-color:white;" colspan="1">CC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256040.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256041.png" /></td> <td colname="5" style="background-color:white;" colspan="1">CCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256042.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256043.png" /></td> <td colname="5" style="background-color:white;" colspan="1">CCCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256044.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XIV</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256045.png" /></td> <td colname="5" style="background-color:white;" colspan="1">IO or D</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256046.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XV</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256047.png" /></td> <td colname="5" style="background-color:white;" colspan="1">DC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256048.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XVI</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256049.png" /></td> <td colname="5" style="background-color:white;" colspan="1">DCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256050.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XVII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256051.png" /></td> <td colname="5" style="background-color:white;" colspan="1">DCCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256052.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XVIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256053.png" /></td> <td colname="5" style="background-color:white;" colspan="1">DCCCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256054.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XIX</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256055.png" /></td> <td colname="5" style="background-color:white;" colspan="1">CIO or M</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256056.png" /></td> <td colname="2" style="background-color:white;" colspan="1">XX</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256057.png" /></td> <td colname="5" style="background-color:white;" colspan="1">CIOCIO or MM</td> </tr> </tbody> </table>
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A partial list of Roman numerals is:<table border="0" cellpadding="0" cellspacing="0" style="background-color:black;"> <tr><td> <table border="0" cellspacing="1" cellpadding="4" style="background-color:black;"> <tbody> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  1 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">I</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  30 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">XXX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  2 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">II</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  40 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">XL or XXXX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  3 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">III</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  50 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">L</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  4 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">IV or IIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  60 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">LX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  5 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">V</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  70 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">LXX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  6 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">VI</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  80 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">LXXX</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  7 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">VII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  90 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">XC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  8 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">VIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  99 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">XCIX or IC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  9 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">IX or VIIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  100 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">C</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  10 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">X</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  101 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">CI</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  11 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XI</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  200 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">CC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  12 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  300 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">CCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  13 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  400 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">CCCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  14 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XIV</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  500 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">IO or D</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  15 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XV</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  600 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">DC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  16 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XVI</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  700 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">DCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  17 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XVII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  800 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">DCCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  18 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XVIII</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  900 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">DCCCC</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  19 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XIX</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  1000 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">CIO or M</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  20 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">XX</td> <td colname="3" style="background-color:white;" colspan="1"></td> <td colname="4" style="background-color:white;" colspan="1"> $  2000 $
 +
</td> <td colname="5" style="background-color:white;" colspan="1">CIOCIO or MM</td> </tr> </tbody> </table>
  
 
</td></tr> </table>
 
</td></tr> </table>
  
''''''<table border="0" cellpadding="0" cellspacing="0" style="background-color:black;"> <tr><td> <table border="0" cellspacing="1" cellpadding="4" style="background-color:black;"> <tbody> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256058.png" /></td> <td colname="2" style="background-color:white;" colspan="1">IOO</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256059.png" /></td> <td colname="2" style="background-color:white;" colspan="1">CCIOO</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256060.png" /></td> <td colname="2" style="background-color:white;" colspan="1">CCCIOOO</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256061.png" /></td> <td colname="2" style="background-color:white;" colspan="1">IOOOO</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r082/r082560/r08256062.png" /></td> <td colname="2" style="background-color:white;" colspan="1">CCCCIOOOO</td> </tr> </tbody> </table>
+
<table border="0" cellpadding="0" cellspacing="0" style="background-color:black;"> <tr><td> <table border="0" cellspacing="1" cellpadding="4" style="background-color:black;"> <tbody> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  5000 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">IOO</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  10000 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">CCIOO</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  100000 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">CCCIOOO</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  500000 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">IOOOO</td> </tr> <tr> <td colname="1" style="background-color:white;" colspan="1"> $  1000000 $
 +
</td> <td colname="2" style="background-color:white;" colspan="1">CCCCIOOOO</td> </tr> </tbody> </table>
  
 
</td></tr> </table>
 
</td></tr> </table>

Latest revision as of 08:12, 6 June 2020


A medieval system developed from a cruder Roman system. The system of Roman numerals is based on using special symbols to denote decimal digits $ I = 1 $, $ X = 10 $, $ C = 100 $, $ M = 1000 $, and their halves $ V = 5 $, $ L = 50 $, $ D = 500 $. Positive integers are written by repeating these numerals. When a letter is followed by a letter of lesser value, the values are added (addition principle), when a letter is followed by a letter of greater value, the smaller is subtracted from the larger (subtraction principle). The latter rule is only applied in order to prevent a fourfold repetition of the same letter. In this system it is rather inconvenient to carry out arithmetic operations with multi-digit numerals. At present, the Roman numerals are no longer used, except in certain cases such as the designation of centuries and years A.D. and also months when designating dates, ordinal numbers and sometimes derivatives of low order higher than three: $ y ^ {IV } , y ^ {V} $, etc.

Comments

The cruder Roman system referred to above is as follows: $ 1000 $ was represented by $ 1 $ between parenthesis: $ ( 1) $; $ 10 000 $ was represented by $ (( 1)) $, etc. Later $ ( 1) $ became $ M $. Half of it, $ {} 1) $, later became $ D $.

A partial list of Roman numerals is:

<tbody> </tbody>
$ 1 $ I $ 30 $ XXX
$ 2 $ II $ 40 $ XL or XXXX
$ 3 $ III $ 50 $ L
$ 4 $ IV or IIII $ 60 $ LX
$ 5 $ V $ 70 $ LXX
$ 6 $ VI $ 80 $ LXXX
$ 7 $ VII $ 90 $ XC
$ 8 $ VIII $ 99 $ XCIX or IC
$ 9 $ IX or VIIII $ 100 $ C
$ 10 $ X $ 101 $ CI
$ 11 $ XI $ 200 $ CC
$ 12 $ XII $ 300 $ CCC
$ 13 $ XIII $ 400 $ CCCC
$ 14 $ XIV $ 500 $ IO or D
$ 15 $ XV $ 600 $ DC
$ 16 $ XVI $ 700 $ DCC
$ 17 $ XVII $ 800 $ DCCC
$ 18 $ XVIII $ 900 $ DCCCC
$ 19 $ XIX $ 1000 $ CIO or M
$ 20 $ XX $ 2000 $ CIOCIO or MM
<tbody> </tbody>
$ 5000 $ IOO
$ 10000 $ CCIOO
$ 100000 $ CCCIOOO
$ 500000 $ IOOOO
$ 1000000 $ CCCCIOOOO

References

[a1] G. Friedlein, "Die Zahlzeichen und das elementare Rechnen der Griechen und Römer und des Christlichen Abendlandes von 7. bis 13. Jahrhundert" , Schaan, reprint (1982)
[a2] G. Ifrah, "From one to zero: a universal history of numbers" , Penguin (1987) (Translated from French)
[a3] F. Cajori, "A history of mathematical notations" , 1 , Open Court (1974)
How to Cite This Entry:
Roman numerals. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Roman_numerals&oldid=48583
This article was adapted from an original article by BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article