Mathematical Symbols - Roman Symbols (One to Ten Thousand)

Mathematical Roman Symbols are very important to learn the number system in mathematics, on using symbols we can easily understand the concepts of topics. 

Generally, Mathematical Symbols can be categorized on their importance in the following ways:

1. Mathematics symbols - Number
2. Mathematics symbols - Basic
3. Mathematics symbols - Algebraic
4. Mathematics symbols - Geometric
5. Mathematics symbols - Trigonometry
6. Mathematics symbols - Set Theory
7. Mathematics symbols - Statistics & Probability
8. Mathematics symbols - Calculus And Analysis 
9. Mathematics symbols - Logical and Reasoning
10. Mathematics symbols - Roman Symbols
11. Mathematics symbols - Greek Symbols
12. Mathematics symbols - Miscellaneous 

Now we shall learn /discuss the tenth topic of Mathematical symbols - Roman Symbols on this post.

Mathematics symbols - Roman Symbols

 These are very important Basic Tools frequently used by us not only in Airthematic but also in Management as well as in other branches of applied mathematical sciences and engineering.

Thousands a year ago Romans had a unique system of numbers which had only SEVEN symbols, Each having different values are such as:-

Roman Numerals	Value
I	1
V	5
X	10
L	50
C	100
D	500
M	1000

Note- For 0 (Zero) there are no symbols in Roman Numerals.

 Rules for writing Roman symbols

Rule 1- I, X, and C Roman digits are repeated up to three times in succession to form the numbers that is cannot be repeated up to four times. 

For illustrations we consider the following examples:

Example 1:

I = 1

II = 1 + 1 = 2

III = 1 + 1 + 1 = 3 (It is valid since used up to three times only.)

IIII = 1 + 1 + 1 + 1 = 4 is wrong

Example 2:

X = 10

XX = 10 + 10 = 20

XXX = 10 + 10 + 10 = 30 (It is valid since used up to three times only.)

XXXX = 10 + 10 + 10 + 10 = 40 is wrong 

Example 3:

C = 100

CC = 100 + 100 = 200

CCC = 100 + 100 + 100 = 300 (It is valid since used up to three times only.)

CCCC = 100 + 100 + 100 + 100 = 400 is wrong since repeated more than three times.

Rule 2- V, L, and D Roman digits are not repeated in succession to form the numbers that are the repetition of V, L, and D are not allowed. 

so instead of using X for 10, VV is not correct. (VV = 10 is wrong)

Rule 3- If the digit of lower value is written to the right or after / later of the digit of higher value, all the digits of numbers are added.

Illustrations:-

VI = 5  + 1 = 6

VII = 5  + 2 =7

VIII = 5  + 3 =8

XI = 10  + 1 =11

Rule 4- If the digit of lower value is written to the left or ago / before the digit of higher value, then the lower numerals or digits are subtracted from higher values.

Illustrations:-

IV = 5 - 1 = 4

IX = 10 - 1 = 9

1XX = 20 - 1 = 19

XC = 100 - 10 =90

Rule 5 -  Multiplication rule

If a vinculum or horizontal line is drawn over the digit of Roman numerals or symbols, then the value of the numerals becomes one thousand ( 1000) times.

Illustrations:-

IV = 4 then   = 4000
V = 5  then     ⊽  =  50000
VI = 6 then   = 6000
VII = 7  then       =  7000
VIII = 8 then   = 8000
IX = 9 then   = 9000
X = 10  then       =  10000

Some important Roman Symbols up to 10000 are listed below in the table on behalf of this we can write all numbers up to 10000 with the help of illustrations below the table.

Table of important Mathematical Symbol of  Roman Symbols

Number	Roman Numeral	Justification
0	NOT DEFINED
1	I	1+1
2	II	1+1+1
3	III	1+1+1
4	IV	5 -1  (IIII is wrong since I used four times.)
5	V	5
6	VI	5 + 1
7	VII	5 + 1 + 1
8	VIII	5 + 1 + 1
9	IX	10 - 1  (VIIII is wrong since I used four times.)
10	X	10
11	XI	10+1
12	XII	10+1+1
13	XIII	10+1+1+1
14	XIV	10+(5-1)
15	XV	10+5
16	XVI	10+5+1
17	XVII	10+5+1+1
18	XVIII	10+5+1+1+1
19	XIX	10+(10-1)
20	XX	10+10
21	XXI	10+10+1
22	XXII	10+10+1+1
23	XXIII	10+10+1+1+1
24	XXIV	10+10+(5-1)
25	XXV	10+10+5
26	XXVI	10+10+5+1
27	XXVII	10+10+5+1+1
28	XXVIII	10+10+5+1+1+1
29	XXIX	10+10+(10-1)
30	XXX	10+10+10
31	XXXI	10+10+10+1
32	XXXII	10+10+10+1+1
33	XXXIII	10+10+10+1+1+1
34	XXXIV	10+10+10+(5-1)
35	XXXV	10+10+10+5
36	XXXVI	10+10+10+5+1
37	XXXVII	10+10+10+5+1+1
38	XXXVIII	10+10+10+5+1+1+1
39	XXXIX	10+10+10+(10-1)
40	XL	50-10  (XXXX is wrong since X is used four times.)
41	XLI	(50-10)+1
42	XLII	(50-10)+1+1
43	XLIII	(50-10)+1+1
44	XLIV	(50-10)+(5-1)
45	XLV	(50-10)+5
46	XLVI	(50-10)+5+1
47	XLVII	(50-10)+5+1+1
48	XLVIII	(50-10)+5+1+1+1
49	XLIX	(50-10)+(10-1)
50	L	50
51	LI	50+1
52	LII	50+1+1
53	LIII	50+1+1+1
54	LIV	50+(5-1)
55	LV	50+5
56	LVI	50+5+1
57	LVII	50+5+1+1
58	LVIII	50+5+1+1+1
59	LIX	50+(10-1)
60	LX	50+10
61	LXI	50+10+1
62	LXII	50+10+1+1
63	LXIII	50+10+1+1+1
64	LXIV	50+10+(5-1)
65	LXV	50+10+5
66	LXVI	50+10+5+1
67	LXVII	50+10+5+1+1
68	LXVIII	50+10+5+1+1+1
69	LXIX	50+10+(10-1)
70	LXX	50+10+10
71	LXI	50+10+10+1
72	LXXII	50+10+10+1+1
73	LXXIII	50+10+10+1+1+1
74	LXXIV	50+10+10+(5-1)
75	LXXV	50+10+10+5
76	LXXVI	50+10+10+5+1
77	LXXVII	50+10+10+5+1+1
78	LXXVIII	50+10+10+5+1+1+1
79	LXXIX	50+10+10+(10-1)
80	LXXX	50+10+10+10
81	LXXXI	50+10+10+10+1
82	LXXXII	50+10+10+10+1+1
83	LXXXIII	50+10+10+10+1+1+1
84	LXXXIV	50+10+10+10+(5-1)
85	LXXXV	50+10+10+10+5
86	LXXXVI	50+10+10+10+5+1
87	LXXXVII	50+10+10+10+5+1+1
88	LXXXVIII	50+10+10+10+5+1+1+1
89	LXXXIX	50+10+10+10+(10-1)
90	XC	100-10  (LXXXX is wrong since X is used four times.)
91	XCI	(100-10)+1
92	XCII	(100-10)+1+1
93	CXIII	(100-10)+1+1+1
94	CXIV	(100-10)+(5-1)
95	CXV	(100-10)+5
96	XCVI	(100-10)+5+1
97	XCVII	(100-10)+5+1+1
98	XCVIII	(100-10)+5+1+1+1
99	XCIX	(100-10)+(10-1)
100	C	100
200	CC	100+100
300	CCC	100+100+100
400	CD	500-100 (CCCC is wrong since C is used four times.)
500	D	500
600	DC	500+100
700	DCC	500+100+100
800	DCCC	500+100+100+100
900	CM	1000-100
1000	M	1000
1100	MC	1000+100
1200	MCC	1000+100+100
1300	MCCC	1000+100+100+100
1400	MCD	1000+(500-100)
1500	MD	1000+500
1600	MDC	1000+500+100
1700	MDCC	1000+500+100+100
1800	MDCCC	1000+500+100+100+100
1900	MCM	1000+(1000-100)
2000	MM	1000+1000
2100	MMC	1000+1000+100
2200	MMCC	1000+1000+100+100
2300	MMCCC	1000+1000+100+100+100
2400	MMCD	1000+1000+(500-100)
2500	MMD	1000+1000+500
2600	MMDC	1000+1000+500+100
2700	MMDCC	1000+1000+500+100+100
2800	MMDCCC	1000+1000+500+100+100+100
2900	MMCM	1000+1000+(1000-100)
3000	MMM	1000+1000+1000

Table of important Mathematical Symbol - Roman Symbols Greater than 3000

Number	Roman Numeral	Justification
3100	MMMC	1000+1000+1000+100
3200	MMMCC	1000+1000+1000+100+100
3300	MMMCCC	1000+1000+1000+100+100+100
3400	MMMCD	1000+1000+1000+(500-100)
3500	MMMD	1000+1000+1000+500
3600	MMMDC	1000+1000+1000+500+100
3700	MMMDCC	1000+1000+1000+500+100+100
3800	MMMDCCC	1000+1000+1000+500+100+100
3900	MMMCM	1000+1000+1000+(1000-100)
4000		4*1000=4000  (By Multiplication Rule)
4100	C	4000+100
4200	CC	4000+100+100
4300	CCC	4000+100+100+100
4400	CD	4000+(500-100)
4500	D	4000+500
4600	DC	4000+500+100
4700	DCC	4000+500+100+100
4800	DCCC	4000+500+100+100+100
4900	CM	4000+(1000-100)
5000	⊽	5*1000
5100	⊽C	5000+100
5200	⊽CC	5000+100+100
5300	⊽CCC	5000+100+100+100
5400	⊽CD	5000+(500-100)
5500	⊽D	5000+500
5600	⊽DC	5000+500+100
5700	⊽DCC	5000+500+100+100
5800	⊽DCCC	5000+500+100+100
5900	⊽CM	5000+(1000-100)
6000		6 *1000
6100	C	6000+100
6200	CC	6000+100+100
6300	CCC	6000+100+100+100
6400	CD	6000+(500-100)
6500	D	6000+500
6600	DC	6000+500+100
6700	DCC	6000+500+100+100
6800	DCCC	6000+500+100+100+100
6900	CM	6000+(1000-100)
7000		7*1000
7100	C	7000+100
7200	CC	7000+100+100
7300	CCC	7000+100+100+100
7400	CD	7000+(500-100)
7500	D	7000+500
7600	DC	7000+500+100
7700	DCC	7000+500+100+100
7800	DCCC	7000+500+100+100+100
7900	DCM	7000+(10000-100)
8000		8*1000
8100	C	8000+100
8200	CC	8000+100+100
8300	CCC	8000+100+100+100
8400	CD	8000+(500-100)
8500	D	8000+500
8600	DC	8000+500+100
8700	DC	8000+500+100+100
8800	DCC	8000+500+100+100+100
8900	CM	8000+(1000-100)
9000		9*1000
9100	C	9000+100
9200	CC	9000+100+100
9300	CCC	9000+100+100+100
9400	CD	9000+(500-100)
9500	DC	9000+500
9600	DC	9000+500+100
9700	DCC	9000+500+100+100
9800	DCCC	9000+500+100+100+100
9850	DCCCL	9000+500+100+100+100+50
9900	CM	9000+(1000-100)
9950	CML	9000+(1000-100)+50
10000		10*1000

We can use the above rules to write some numerals/numbers in Roman symbols with the help of following illustrations and vice versa are such as:

Illustrations 1:- Write the Roman Symbols for the following numerals/numbers, with justifications?

(I) 111 = CXI =100 +10+1

(II) 121 = CXXI =100 +10+10+1 

(III) 129 = CXXIX =100 +10+10+(10-1) 

(IV) 135 = CXXXV =100 +10+10+10+5 

(V) 149 = CXLIX  =100 +(50-10)+(10-1)

(VI) 151 = CLI =100 +50+1

(VII) 159 = CLIX =100 +50+(10-1)

(VIII) 173 = CLXXIII =100 +50+10+10+1+1+1

(IX) 189 = CLXXXIX =100 +50+10+10+10+(10-1) 

(X) 199 = CXCIX =100 +(100-10)+(10-1) 

Illustrations 2:- Write the Roman Symbols for the following numerals/numbers, with justifications?

(I) 212 = CCXII =100 +100+10+1+1

(II) 223 = CXXIII =100 +100+10+10+1+1+1 

(III) 229 = CCXXIX =100+100 +10+10+(10-1) 

(IV) 236 = CCXXXVI =100 +100+10+10+10+5+1 

(V) 249 = CCXLIX  =100 +100+(50-10)+(10-1)

(VI) 254 = CCLIV =100 +100+50+(5-1)

(VII) 259 = CCLIX =100 +100+50+(10-1)

(VIII) 272 = CCLXXII =100 +100+50+10+10+1+1

(IX) 289 = CCLXXXIX =100+100 +50+10+10+10+(10-1) 

(X) 294 = CCXCIV =100+100 +(100-10)+(5-1) 

Illustrations 3:- Write the Roman Symbols for the following numerals/numbers, with justifications?

(I) 313 = CCCXIII =100 +100+100+10+1+1+1

(II) 323 = CCCXXIII =100 +100+100+10+10+1+1+1 

(III) 329 = CCCXXIX =100+100+100 +10+10+(10-1) 

(IV) 337 = CCXXXVII =100+100 +100+10+10+10+5+1+1 

(V) 349 = CCCXLIX  =100 +100+100+(50-10)+(10-1)

(VI) 354 = CCCLIV =100+100 +100+50+(5-1)

(VII) 359 = CCCLIX =100+100 +100+50+(10-1)

(VIII) 373 = CCCLXXIII =100 +100+100+50+10+10+1+1+1

(IX) 389 = CCCLXXXIX =100+100+100 +50+10+10+10+(10-1) 

(X) 398 = CCCXCVIII =100+100 +100+(100-10)+5+1+1+1

Illustrations 4:- Write the Roman Symbols for the following numerals/numbers, with justifications?

(I) 413 = CDXIII =(500-100)+10+1+1+1

(II) 428 = CDXXVIII =(500 -100)+10+10+5+1+1+1 

(III) 529 = DXXIX =500 +10+10+(10-1) 

(IV) 537 = DXXXVII =500+10+10+10+5+1+1 

(V) 549 = DXLIX  =500+(50-10)+(10-1)

(VI) 454 = CDLIV =(500-100)+50+(5-1)

(VII) 369 = CCCLXIX =100+100 +100+50+10+(10-1)

(VIII) 573 = DLXXIII =500+50+10+10+1+1+1

(IX) 489 = CDLXXXIX = (500-100) +50+10+10+10+(10-1) 

(X) 598 = DXCVIII =500+(100-10)+5+1+1+1
      We can use like above illustrations to write any numerals up to 10000 into Roman Symbols.
__________________________________________________