ROMAN NUMERALS

 

ROMAN NUMERALS

Look at the wall clock which is on the left side. Observe the numbers on it. We use those numbers. See the wall clock which is on the right side and observe the numbers which are on it. They are the numbers which were being used by Romans. Hence they are called Roman Numerals. Even now we can see the Roman numerals in some books and in clocks.

          

 

List given below shows the use of seven symbols and their equivalents in Hindu-Arabic.

Using these symbols Romans were writing from 1 to 50 and they are

Roman Numbers	I	V	X	L	C	D	M
Hindu-Arabic Numerals	1	5	10	50	100	500	1000

Given below

The following rules are given to help you to read and write the numerals in the Roman system.

 

Hindu Arabic	Roman	Hindu Arabic	Roman	Hindu Arabic	Roman	Hindu Arabic	Roman	Hindu Arabic	Roman
1	I	11	XI	21	XXI	31	XXXI	41	XLI
2	II	12	XII	22	XXII	32	XXXII	42	XLII
3	III	13	XIII	23	XXIII	33	XXXIII	43	XLIII
4	IV	14	XIV	24	XXIV	34	XXXIV	44	XLIV
5	V	15	XV	25	XXV	35	XXXV	45	XLV
6	VI	16	XVI	26	XXVI	36	XXXVI	46	XLVI
7	VII	17	XVII	27	XXVII	37	XXXVII	47	XLVII
8	VIII	18	XVIII	28	XXVIII	38	XXXVIII	48	XLVIII
9	IX	19	XIX	29	XXIX	39	XXXIX	49	XLIX
10	X	20	XX	30	XXX	40	XL	50	L

 

Hindu Arabic	Roman	Hindu Arabic	Roman	Hindu Arabic	Roman	Hindu Arabic	Roman	Hindu Arabic	Roman
51	LI	61	LXI	71	LXXI	81	LXXXI	91	XCI
52	LII	62	LXII	72	LXXII	82	LXXXII	92	XCII
53	LIII	63	LXIII	73	LXXIII	83	LXXXIII	93	XCIII
54	LIV	64	LXIV	74	LXXIV	84	LXXXIV	94	XCIV
55	LV	65	LXV	75	LXXV	85	LXXXV	95	XCV
56	LVI	66	LXVI	76	LXXVI	86	LXXXVI	96	XCVI
57	LVII	67	LXVII	77	LXXVII	87	LXXXVII	97	XCVII
58	LVIII	68	LXVIII	78	LXXVIII	88	LXXXVIII	98	XCVIII
59	LIX	69	LXIX	79	LXXIX	89	LXXXIX	99	XCIX
60	LX	70	LXX	80	LXXX	90	XC	100	C

 

 

Hindu Arabic	Roman	Hindu Arabic	Roman	Hindu Arabic	Roman
1	I	18	XVIII	700	DCC
2	II	19	XIX	800	DCCC
3	III	20	XX	900	CM
4	IV	25	XXV	1,000	M
5	V	30	XXX	1,100	MC
6	VI	40	XL	1,200	MCC
7	VII	50	L	1,300	MCCC
8	VIII	60	LX	1,400	MCD
9	IX	70	LXX	1,500	MD
10	X	80	LXXX	1,600	MDC
11	XI	90	XC	1,700	MDCC
12	XII	100	C	1,800	MDCCC
13	XIII	200	CC	1,900	MCM
14	XIV	300	CCC	2,000	MM
15	XV	400	CD	10,000	x̄
16	XVI	500	D	1,00,000	C̄
17	XVII	600	DC	2024	MMXXIV

 

 

Rule 1: Numerals of the same value such as I,X,C,M are added.

Ex: III = 3, XXX = 30, MMM = 3000.

CCC = 300.

These symbols cannot be repeated more than 3 times in a number.

Ex: IIII is written as IV.

XXXX is written as XL.

 

Rule 2: Numerals V, L, D are not repeated

Ex: VV is written as X.

LL is written as C.

 

Rule 3: A smaller numeral written to the right of a numeral of greater value is always added to the greater numeral.

Ex: XV = X+V =10+5 = 15.

LXXV = L+X+X+V = 50+10+10+5 =75.

DC = D+C = 500+100 = 600.

 

Rule 4: A smaller numeral written to the left of a numeral of greater value is always subtracted from the greater numeral immediately following it.

Ex: IV = V-I = 5-1 =4.

IX = X-I = 10-1 = 9.

CD = D-C =500 -100 = 400

 

Points to be remembered while subtraction:

i) From V and X only I may be subtracted.

ii) From L and C only X may be subtracted.

iii) From D and M only C may be subtracted.

iv) V.L.D cannot be subtracted from anything.

 

Example:

Observe: IV, IX, XL, XC, CD, CM may be written but IL, IC, ID, ….XD, XM,….VC, VD, cannot be written.

 

Rule 5: First Rule IV should be followed and then rule III should be followed in the following case.

“While writing the numbers, if smaller values symbol comes in between two greater values”.

Example:

i) XIX = X+(IX) = X+(X-I) = 10 + (10-1) = 10+9 = 19.

ii) LIX = L+(IX) = L+(X-I) = 50 + (10-1) = 50 + 9 = 59.

 

Observe: XIX = 19; XIX ¹ 21

Under the above frame work of rules, we can write all the number under the Roman system.

 

Example 1: Write 1988 in Roman Numerals.

1988 = 1000 + 900 + 80 + 8

= 1000 + (1000 -100) + 50 + 10 + 10 + 10 + 8

= MCMLXXXVIII

 

Example 2: Write MMCDXXXIV in Base Ten System MM = 2000; CD = 400; XXX = 30; IV = 4.

MMCDXXXIV = 2434.

 

Observe:

1. No place value in Roman Numerals.

2. There is no concept of ‘0’ in Roman system as we have in decimal system.

3. Hence it is very complicated to write large numbers and also to do mathematical operations.

 

Exercise:

1. Write the following in Hindu-Arabic Numerals.

a) XXIV - 24

b) LXXII - 62

c) CLXV - 165

d) XLIX - 49

e) CCCVIII - 308

f) CCCXCVII - 397

g) MDCCCXVIII - 1818

h) MMCCCXXX - 2330

i) MMCDXCVI - 2496

j) MMCMXLIX - 2949

2. Write the following in Roman Numerals.

a) 38 - XXXVIII

b) 79 - LXXIX

c) 276 - CCLXXVI

d) 2222 - MMCCXXII

e) 505 - DV

f) 1616 - MDCXVI

 

3. Pick out the correct one and write.

a) 99 is written in Roman Numerals as

i) LXXXXIX

ii) XCIX

iii) IC

iv) XXXXXXXXXIX

 

b) LI is written in Hindu-Arabic numerals as

i) 501

ii) 49

iii) 51

iv) 5001

 

4. Which of the following do not give meaning.

a) CCI

b) IXIV

c) LCXVI

d) ICC

e) CCCI

f) LM

 

5. Match the following:

 

Hindu Arabic	Roman
139	CXLVIII
155	CLXV
148	CXXXIX
199	CLXXV
175	CXCIX
165	CLV

 

Ans:

Hindu Arabic	Roman
139	CXXXIX
155	CLV
148	CXLVIII
199	CXCIX
175	CLXXV
165	CLXV

 

 

6. Write the numbers in Roman Numerals.

a) India became Republic in 1950.

b) The velocity of sound in water per second is 1480 metres.

c) Gandhiji was born in 1869.