Roman Numerals

Objective 

This topic will teach us about the Roman Numeral system and the rules of the system. 

Roman Numerals

We have been using the Hindu-Arabic numeral system so far. This is not the only system available. 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 the use of Roman numerals in clocks; it is also used for classes in the school time table etc. 

Roman numerals are expressed by seven letters of the alphabet.  These are shown in the table below along with the number they represent. 

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

 The Roman numerals: I, II, III, IV, V, VI, VII, VIII, IX, X denote 1,2,3,4,5,6,7,8,9 and 10 respectively. This is followed by XI for 11, XII for 12,... till XX for 20.  

Rules of the System

The rules for the system are :

  1. If a symbol is repeated, its value is added as many times as it occurs: i.e. II equals 2, XX is 20 and XXX is 30.
  2. A symbol is repeated three times but not more than that. However, the symbols V, L and D are never repeated.
  3. 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.
    VI = 5 + 1 = 6, XII = 10 + 2 = 12 and LXV = 50 + 10 + 5 = 65
  4. 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.
    IV = 5 – 1 = 4, IX = 10 – 1 = 9
    XL= 50 – 10 = 40, XC = 100 – 10 = 90
  5. The symbols V, L and D are never written to the left of a symbol of greater value, i.e. V, L and D are never subtracted. The symbol I can be subtracted from V and X only. The symbol X can be subtracted from L, M and C only. 

Following these rules we get, 

Arabic Numerals Roman Numerals Arabic Numerals Roman Numerals Arabic Numerals Roman Numerals
1 I 11 XI 30 XXX
2 II 12 XII 40 XL
3 III 13 XIII 50 L
4 IV 14 XIV 60 LX
5 V 15 XV 70 LXX
6 VI 16 XVI 80 LXXX
7 VII 17 XVII 90 XC
8 VIII 18 XVIII 100 C
9 IX 19 XIX 500 D
10 X 20 XX 1000 M

Let us look at an example of writing in Roman Numerals for the numbers 69 and 98.

69
= 60 + 9
= (50 + 10) + 9
= LX + IX
= LX IX 

98
= 90 + 8
= (100 – 10) + 8
= XC + VIII
= LX IX = XCVIII 

Summary 

We use the Hindu-Arabic system of numerals and we have learnt another system of writing numerals, which is the Roman system. 

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