Roman Numerals

One of the early systems of writing numerals is the system of Roman numerals. This system is still used in many places. For example,

  • we can see Roman numerals in clocks
  • they are used to number pages that come before the main pages of a book
  • they are used to identify kings and queens (for example, Henry VIII of England)
  • they are used to identify sporting events (like, The New York Giants won Super Bowl XLII).

They use the following seven letters of the alphabet to write all numbers.

IVXLCDM
1510501005001000

There is no zero (0) in the Roman system. The Roman system does not use place value concept. The Roman numerals I, II, III, IV, V, VI, VII, VIII, IX, X respectively denote 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. This is followed by XI for 11, XII for 12, . . . , till XX for 20. The traditional Roman numeral system was only used for numbers up to 3,999 which is represented as MMMCMXCIX.

The rules for the system

(a) If a symbol is repeated, its value is added as many times as it occurs.

For example,

  • II is equal 2
  • XX is 20
  • XXX is 30.

(b) A symbol is not repeated more than three times. But the symbols V, L and D are never repeated.

Hence, IIII, XXXXX are not valid. 

(c) If a symbol of smaller value is written to the right of a symbol of greater value, its value gets added to the value of greater symbol.

For example,

  • VI = 5 + 1 = 6
  • XII = 10 + 2 = 12
  • XXVII = 10 + 10 + 5 + 1 + 1 = 27
  • LXV = 50 + 10 + 5 = 65
  • MDC = 1000 + 500 + 100 = 1600

(d) If a symbol of smaller value is written to the left of a symbol of greater value, its value is subtracted from the value of the greater symbol.

For example,

  • IV = 5 – 1 = 4
  • IX = 10 – 1 = 9
  • XL= 50 – 10 = 40
  • XC = 100 – 10 = 90

(e) The symbols V, L and D are never written to the left of a symbol of greater value. In other words, V, L and D are never subtracted.

(f) The symbol I can be subtracted from V and X only.

(g) The symbol X can be subtracted from L, M and C only.

Example. Write 69 in Roman Numerals.

Solution. We can write

69 = 60 + 9

= (50 + 10) + 9

= LX + IX

= LXIX

Example. Write 98 in Roman Numerals98.

Solution. We can write

98 = 90 + 8

= (100 – 10) + 8

= XC + VIII

= XCVIII

Example. Can we write 40 as XXXX?

Solution. No.

As we cannot repeat the symbol X for more than three times.

Example. How to write 800 in Roman numeral?

Solution. We can write, 800 = 500 + 100 + 100 + 100

We know that, 500 = D and 100 = C.

Therefore, 800 = DCCC.

Example. Write 3249 in the Roman number system.

Solution. We can write

3249

= 3000 + 200 + 40 + 9

= MMM + CC + XL + IX

= MMMCCXLIX

Example. Write MDCLXVII in the Hindu-Arabic system.

Solution. We can write

MDCLXVII

= M + DC + LX + VII

= 1000 + 600 + 60 + 7

= 1667

Below is the list of all Roman numerals up to 1000.

Roman Numerals 1 to 100

1I34XXXIV67LXVII
2II35XXXV68LXVIII
3III36XXXVI69LXIX
4IV37XXXVII70LXX
5V38XXXVIII71LXXI
6VI39XXXIX72LXXII
7VII40XL73LXXIII
8VIII41XLI74LXXIV
9IX42XLII75LXXV
10X43XLIII76LXXVI
11XI44XLIV77LXXVII
12XII45XLV78LXXVIII
13XIII46XLVI79LXXIX
14XIV47XLVII80LXXX
15XV48XLVIII81LXXXI
16XVI49XLIX82LXXXII
17XVII50L83LXXXIII
18XVIII51LI84LXXXIV
19XIX52LII85LXXXV
20XX53LIII86LXXXVI
21XXI54LIV87LXXXVII
22XXII55LV88LXXXVIII
23XXIII56LVI89LXXXIX
24XXIV57LVII90XC
25XXV58LVIII91XCI
26XXVI59LIX92XCII
27XXVII60LX93XCIII
28XXVIII61LXI94XCIV
29XXIX62LXII95XCV
30XXX63LXIII96XCVI
31XXXI64LXIV97XCVII
32XXXII65LXV98XCVIII
33XXXIII66LXVI99XCIX
    100C

Roman Numerals 101 to 200

101CI134     CXXXIV167CLXVII
102CII135CXXXV168CLXVIII
103CIII136CXXXVI169CLXIX
104CIV137CXXXVII170CLXX
105CV138CXXXVIII171CLXXI
106CVI139CXXXIX172CLXXII
107CVII140CXL173CLXXIII
108CVIII141CXLI474CLXXIV
109CIX142CXLII175CLXXV
110CX143CXLIII176CLXXVI
111CXI144CXLIV177CLXXVII
112CXII145CXLV178CLXXVIII
113CXIII146CXLVI179CLXXIX
114CXIV147CXLVII180CLXXX
115CXV148CXLVIII181CLXXXI
116CXVI449CXLIX182CLXXXII
117CXVII150CL183CLXXXIII
118CXVIII151CLI184CLXXXIV
119CXIX152CLII185CLXXXV
120CXX153CLIII186CLXXXVI
121CXXI154CLIV187CLXXXII
122CXXII155CLV188CLXXXVIII
123CXXIII156CLVI189CLXXXIX
424CXXIV157CLVII190CXC
125CXXV158CLVIII191CXCI
126CXXVI159CLIX192CXCII
127CXXVII160CLX193CXCIII
128CXXVIII161CLXI194CXCIV
129CXXIX162CLXII195CXCV
130CXXX163CLXIII196CXCVI
131CXXXI164CLXIV197CXCVII
132CXXXII165CLXV198CXCVIII
133CXXXIII166CLXVI499CXCIX
    200CC

Roman Numerals 201 to 300

201CCI234CCXXXIV267CCLXVII
202CCII235CCXXXV268CCLXVIII
203CCIII236CCXXXVI269CCLXIX
204CCIV237CCXXXVII270CCLXX
205CCV238CCXXXVIII271CCLXXI
206CCVI239CCXXXIX272CCLXXII
207CCVII240CCXL273CCLXXIII
208CCVIII241CCXLI274CCLXXIV
209CCIX242CCXLII275CCLXXV
210CCX243CCXLIII276CCLXXVI
211CCXI244CCXLIV277CCLXXVII
212CCXII245CCXLV278CLXXVIII
213CCXIII246CCXLVI279CCLXXIX
214CCXIV247CCXLVII280CCLXXX
215CCXV248CCXLVIII281CCLXXXI
216CCXVI249CCXLIX282CCLXXXII
217CCXVII250CCL283CCLXXXIII
218CCXVIII251CCLI284CCLXXXIV
219CCXIX252CCLII285CCLXXXV
220CCXX253CCLIII286CCLXXXVI
221CCXXI254CCLIV287CCLXXXII
222CCXXII255CCLV288CCLXXXVIII
223CCXXIII256CCLVI289CCLXXXIX
224CCXXIV257CCLVII290CCXC
225CCXXV258CCLVIII291CCXCI
226CCXXVI259CCLIX292CCXCII
227CCXXVII260CCLX293CCXCIII
228CCXXVIII261CCLXI294CCXCIV
229CCXXIX262CCLXII295CCXCV
230CCXXX263CCLXIII296CCXCVI
231CCXXXI264CCLXIV297CCXCVII
232CCXXXII265CCLXV298CCXCVIII
233CCXXXIII266CCLXVI299CCXCIX
    300CCC

Roman Numerals 301 to 400

301CCCI334CCCXXXIV367CCCLXVII
302CCCII335CCCXXXV368CCCLXVIII
303CCCIII336CCCXXXVI369CCCLXIX
304CCCIV337CCCXXXVII370CCCLXX
305CCCV338CCCXXXVIII371CCCLXXI
306CCCVI339CCCXXXIX372CCCLXXII
307CCCVII340CCCXL373CCCLXXIII
308CCCVIII341CCCXLI374CCCLXXIV
309CCCIX342CCCXLII375CCCLXXV
310CCCX343CCCXLIII376CCCLXXVI
311CCCXI344CCCXLIV377CCCLXXVII
312CCCXII345CCCXLV378CCLXXVIII
313CCCXIII346CCCXLVI379CCCLXXIX
314CCCXIV347CCCXLVII380CCCLXXX
315CCCXV348CCCXLVIII381CCCLXXXI
316CCCXVI349CCCXLIX382CCCLXXXII
317CCCXVII350CCCL383CCCLXXXIII
318CCCXVIII351CCCLI384CCCLXXXIV
319CCCXIX352CCCLII385CCCLXXXV
320CCCXX353CCCLIII386CCCLXXXVI
321CCCXXI354CCCLIV387CCCLXXXII
322CCCXXII355CCCLV388CCCLXXXVIII
323CCCXXIII356CCCLVI389CCCLXXXIX
324CCCXXIV357CCCLVII390CCCXC
325CCCXXV358CCCLVIII391CCCXCI
326CCCXXVI359CCCLIX392CCCXCII
327CCCXXVII360CCCLX393CCCXCIII
328CCCXXVIII361CCCLXI394CCCXCIV
329CCCXXIX362CCCLXII395CCCXCV
330CCCXXX363CCCLXIII396CCCXCVI
331CCCXXXI364CCCLXIV397CCCXCVII
332CCCXXXII365CCCLXV398CCCXCVIII
333CCCXXXIII366CCCLXVI399CCCXCIX
    400CD

Roman Numerals 401 to 500

401CDI434CDXXXIV467CDLXVII
402CDII435CDXXXV468CDLXVIII
403CDIII436CDXXXVI469CDLXIX
404CDIV437CDXXXVII470CDLXX
405CDV438CDXXXVIII471CDLXXI
406CDVI439CDXXXIX472CDLXXII
407CDVII440CDXL473CDLXXIII
408CVIII441CXLI474CLXXIV
409CDIX442CDXLII475CDLXXV
410CDX443CDXLIII476CDLXXVI
411CDXI444CDXLIV477CDLXXVII
412CDXII445CDXLV478CDLXXVIII
413CDXIII446CDXLVI479CDLXXIX
414CDXIV447CDXLVII480CDLXXX
415CDXV448CDXLVIII481CDLXXXI
416CDXVI449CDXLIX482CDLXXXII
417CDXVII450CDL483CDLXXXIII
418CDXVIII451CDLI484CDLXXXIV
419CDXIX452CDLII485CDLXXXV
420CDXX453CDLIII486CDLXXXVI
421CDXXI454CDLIV487CDLXXXII
422CDXXII455CDLV488CDLXXXVIII
423CDXXIII456CDLVI489CDLXXXIX
424CDXXIV457CDLVII490CDXC
425CDXXV458CDLVIII491CDXCI
426CDXXVI459CDLIX492CDXCII
427CDXXVII460CDLX493CDXCIII
428CDXXVIII461CDLXI494CDXCIV
429CDXXIX462CDLXII495CDXCV
430CDXXX463CDLXIII496CDXCVI
431CDXXXI464CDLXIV497CDXCVII
432CDXXXII465CDLXV498CDXCVIII
433CDXXXIII466CDLXVI499CDXCIX
    500D

Roman Numerals 501 to 600

501DI534DXXXIV567DLXVII
502DII535DXXXV568DLXVIII
503DIII536DXXXVI569DLXIX
504DIV537DXXXVII570DLXX
505DV538DXXXVIII571DLXXI
506DVI539DXXXIX572DLXXII
507DVII540DXL573DLXXIII
508DVIII541DXLI574DLXXIV
509DIX542DXLII575DLXXV
510DX543DXLIII576DLXXVI
511DXI544DXLIV577DLXXVII
512DXII545DXLV578DLXXVIII
513DXIII546DXLVI579DLXXIX
514DXIV547DXLVII580DLXXX
515DXV548DXLVIII581DLXXXI
516DXVI549DXLIX582DLXXXII
517DXVII550DL583DLXXXIII
518DXVIII551DLI584DLXXXIV
519DXIX552DLII585DLXXXV
520DXX553DLIII586DLXXXVI
521DXXI554DLIV587DLXXXII
522DXXII555DLV588DLXXXVIII
523DXXIII556DLVI589DLXXXIX
524DXXIV557DLVII590DXC
525DXXV558DLVIII591DXCI
526DXXVI559DLIX592DXCII
527DXXVII560DLX593DXCIII
528DXXVIII561DLXI594DXCIV
529DXXIX562DLXII595DXCV
530DXXX563DLXIII596DXCVI
31DXXXI564DLXIV597DXCVII
532DXXXII565DLXV598DXCVIII
533DXXXIII566DLXVI599DXCIX
    600DC

Roman Numerals 601 to 700

601DCI634DCXXXIV667DCLXVII
602DCII635DCXXXV668DCLXVIII
603DCIII636DCXXXVI669DCLXIX
604DCIV637DCXXXVII670DCLXX
605DCV638DCXXXVIII671DCLXXI
606DCVI639DCXXXIX672DCLXXII
607DCVII640DCXL673DCLXXIII
608DCVIII641DCXLI674DCLXXIV
609DCIX642DCXLII675DCLXXV
610DCX643DCXLIII676DCLXXVI
611DCXI644DCXLIV677DCLXXVII
612DCXII645DCXLV678DCLXXVIII
613DCXIII646DCXLVI679DCLXXIX
614DCXIV647DCXLVII680DCLXXX
615DCXV648DCXLVIII681DCLXXXI
616DCXVI649DCXLIX682DCLXXXII
617DCXVII650DCL683DCLXXXIII
618DCXVIII651DCLI684DCLXXXIV
619DCXIX652DCLII685DCLXXXV
620DCXX653DCLIII686DCLXXXVI
621DCXXI654DCLIV687DCLXXXII
622DCXXII655DCLV688DCLXXXVIII
623DCXXIII656DCLVI689DCLXXXIX
624DCXXIV657DCLVII690DCXC
625DCXXV658DCLVIII691DCXCI
626DCXXVI659DCLIX692DCXCII
627DCXXVII660DCLX693DCXCIII
628DCXXVIII661DCLXI694DCXCIV
629DCXXIX662DCLXII695DCXCV
630DCXXX663DCLXIII696DCXCVI
631DCXXXI664DCLXIV697DCXCVII
632DCXXXII665DCLXV698DCXCVIII
633DCXXXIII666DCLXVI699DCXCIX
    700DCC

Roman Numerals 701 to 800

701DCCI734DCCXXXIV767DCCLXVII
702DCCII735DCCXXXV768DCCLXVIII
703DCCIII736DCCXXXVI769DCCLXIX
704DCCIV737DCCXXXVII770DCCLXX
705DCCV738DCCXXXVIII771DCCLXXI
706DCCVI739DCCXXXIX772DCCLXXII
707DCCVII740DCCXL773DCCLXXIII
708DCCVIII741DCCXLI774DCCLXXIV
709DCCIX742DCCXLII775DCCLXXV
710DCCX743DCCXLIII776DCCLXXVI
711DCCXI744DCCXLIV777DCCLXXVII
712DCCXII745DCCXLV778DCCLXXVIII
713DCCXIII746DCCXLVI779DCCLXXIX
714DCCXIV747DCCXLVII780DCCLXXX
715DCCXV748DCCXLVIII781DCCLXXXI
716DCCXVI749DCCXLIX782DCCLXXXII
717DCCXVII750DCCL783DCCLXXXIII
718DCCXVIII751DCCLI784DCCLXXXIV
719DCCXIX752DCCLII785DCCLXXXV
720DCCXX753DCCLIII786DCCLXXXVI
721DCCXXI754DCCLIV787DCCLXXXII
722DCCXXII755DCCLV788DCCLXXXVIII
723DCCXXIII756DCCLVI789DCCLXXXIX
724DCCXXIV757DCCLVII790DCCXC
725DCCXXV758DCCLVIII791DCCXCI
726DCCXXVI759DCCLIX792DCCXCII
727DCCXXVII760DCCLX793DCCXCIII
728DCCXXVIII761DCCLXI794DCCXCIV
729DCCXXIX762DCCLXII795DCCXCV
730DCCXXX763DCCLXIII796DCCXCVI
731DCCXXXI764DCCLXIV797DCCXCVII
732DCCXXXII765DCCLXV798DCCXCVIII
733DCCXXXIII766DCCLXVI799DCCXCIX
    800DCCC

Roman Numerals 801 to 900

801DCCCI834DCCCXXXIV867DCCCLXVII
802DCCCII835DCCCXXXV868DCCCLXVIII
803DCCCIII836DCCCXXXVI869DCCCLXIX
804DCCCIV837DCCCXXXVII870DCCCLXX
805DCCCV838DCCCXXXVIII871DCCCLXXI
806DCCCVI839DCCCXXXIX872DCCCLXXII
807DCCCVII840DCCCXL873DCCCLXXIII
808DCCCVIII841DCCCXLI874DCCCLXXIV
809DCCCIX842DCCCXLII875DCCCLXXV
810DCCCX843DCCCXLIII876DCCCLXXVI
811DCCCXI844DCCCXLIV877DCCCLXXVII
812DCCCXII845DCCCXLV878DCCCLXXVIII
813DCCCXIII846DCCCXLVI879DCCCLXXIX
814DCCCXIV847DCCCXLVII880DCCCLXXX
815DCCCXV848DCCCXLVIII881DCCCLXXXI
816DCCCXVI849DCCCXLIX882DCCCLXXXII
817DCCCXVII850DCCCL883DCCCLXXXIII
818DCCCXVIII851DCCCLI884DCCCLXXXIV
819DCCCXIX852DCCCLII885DCCCLXXXV
820DCCCXX853DCCCLIII886DCCCLXXXVI
821DCCCXXI854DCCCLIV887DCCCLXXXII
822DCCCXXII855DCCCLV888DCCCLXXXVIII
823DCCCXXIII856DCCCLVI889DCCCLXXXIX
824DCCCXXIV857DCCCLVII890DCCCXC
825DCCCXXV858DCCCLVIII891DCCCXCI
826DCCCXXVI859DCCCLIX892DCCCXCII
827DCCCXXVII860DCCCLX893DCCCXCIII
828DCCCXXVIII861DCCCLXI894DCCCXCIV
829DCCCXXIX862DCCCLXII895DCCCXCV
830DCCCXXX863DCCCLXIII896DCCCXCVI
831DCCCXXXI864DCCCLXIV897DCCCXCVII
832DCCCXXXII865DCCCLXV898DCCCXCVIII
833DCCCXXXIII866DCCCLXVI899DCCCXCIX
    900CM

Roman Numerals 901 to 1000

901CMI934CMXXXIV967CMLXVII
902CMII935CMXXXV968CMLXVIII
903CMIII936CMXXXVI969CMLXIX
904CMIV937CMXXXVII970CMLXX
905CMV938CMXXXVIII971CMLXXI
906CMVI939CMXXXIX972CMLXXII
907CMVII940CMXL973CMLXXIII
908CMVIII941CMXLI974CMLXXIV
909CMIX942CMXLII975CMLXXV
910CMX943CMXLIII976CMLXXVI
911CMXI944CMXLIV977CMLXXVII
912CMXII945CMXLV978CMLXXVIII
913CMXIII946CMXLVI979CMLXXIX
914CMXIV947CMXLVII980CMLXXX
915CMXV948CMXLVIII981CMLXXXI
916CMXVI949CMXLIX982CMLXXXII
917CMXVII950CML983CMLXXXIII
918CMXVIII951CMLI984CMLXXXIV
919CMXIX952CMLII985CMLXXXV
920CMXX953CMLIII986CMLXXXVI
921CMXXI954CMLIV987CMLXXXII
922CMXXII955CMLV988CMLXXXVIII
923CMXXIII956CMLVI989CMLXXXIX
924CMXXIV957CMLVII990CMXC
925CMXXV958CMLVIII991CMXCI
926CMXXVI959CMLIX992CMXCII
927CMXXVII960CMLX993CMXCIII
928CMXXVIII961CMLXI994CMXCIV
929CMXXIX962CMLXII995CMXCV
930CMXXX963CMLXIII996CMXCVI
931CMXXXI964CMLXIV997CMXCVII
932CMXXXII965CMLXV998CMXCVIII
933CMXXXIII966CMLXVI999CMXCIX
    1000M

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