Roman Numerals

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Roman Numerals

What are Roman Numerals?

Roman Numerals are a number system that originated in the ancient Rome that are written by combinations of letters from Latin alphabet. In this system the number we know today are written with letters. Roman numerals use seven letters: I,V, X, L, C, D and M that represents the number 1, 5, 10, 50, 100, 500, 1000.

roman numerals

Rules when operating with roman numerals

First RuleThe roman numerals I,X,C can be repeated only three times when you write a number.

a) We know that I(1), X(10), C(100).

b) We add the value of I, X and C as below.
II = 1 + 1 = 2
XX = 10 + 10 = 20
CC = 100 + 100 =200
III = 1 + 1 + 1
XXX = 10 + 10 + 10 = 30
CCC = 100 + 100 + 100 = 300

c) So the roman numbers I, X and C can’t repeat themselves more than 3 times in a row.

d) The numbers V, L and D can’t repeat themselves because they don’t form roman numerals this way.

Second RuleWhen a number with a smaller value is placed on the right or behind a number with a larger value, the value of all numbers is added.

a) VI = 5 + 1 = 6
VII = 5 + 2 = 7
VIII = 5 + 3 = 8
XI = 10 + 1 = 11
XII = 10 + 2 = 12
XIII = 10 + 3 = 13
XV = 10 + 5 = 15
XVI = 10 + 5 + 1 = 16
LX = 50 + 10 = 60
LXI = 50 + 10 + 1 = 61
LXV = 50 + 10 + 5 = 65
LXVII = 50 + 10 + 5 + 1 + 1 = 67
CLX = 100 + 50 + 10 = 160
CLXVII=100+50+10+50+1+1=167

b) We add the value of similar numbers

II = 1 + 1 = 2
III = 1 + 1 + 1 =3
XX = 10 +10 = 20
XXX = 10 + 10 + 10 = 30
CC = 100 +100 = 200
CCC = 100 + 100 + 100 = 300

 

Third Rule: When a number with a smaller value is placed on the left or before a number with a larger value then the value of the smaller number is subtracted from the value of the larger one.

Be careful!

  • The roman numeral V is never placed before the roman numeral X.

  • The roman numeral L is never placed before the roman numeral C.

  • The roman numeral D is never placed before the roman numeral M.

Fourth RuleIf we want to write roman numerals larger then 10, we have to write the number 10 or the group of number 1 and then the number 1 or 5 depending on the case.

13=10+3=10+1+1+1=XIII

17=10+7=10+5+1+1=XVII

24=20+4=10+10+(5-1)=XXVIII

28=20+8=10+10+5+1+1+1=XXVIII

30=10+10+10=XXX

37=30+7=10+10+10+5+1+1=XXXVII

39=30+9=10+10+10+(10-1)=XXXIX

Based on this model we can also form roman numerals larger than 40.

42=40+2=(50–10)+1+1=XLII

47=40+7=(50–10)+5+1+1=XLVII

53=50+3=50+1+1+1=LIII

1923=1000+900+20+3=1000+(1000-100)+10+10+1+1+1=MCMXXIII

2563=2000+500+60+3=2000+500+50+10+1+1+1=MMDLXII

Large Numbers in Roman

From the table at the beginning we know that the largest number used in roman numerals is M so the largest number we can write using standard numerals is the number 3999.
3999 = MMMCMXCIX
But it’s possible writing roman numerals that are bigger then 3999. If we draw a line across the top of a numeral then we are multiplying it by 1000. The numbers are as in the table below.

roman numerals

Based on the table we can write:

155000 = 100000 + 50000 + 5000 =$\displaystyle \overline{C}\overline{L}\overline{V}$

40963 = 40000 + 900 + 60 + 3 = $\displaystyle \overline{{XXXX}}CMLXIII$

638945 = 600000 + 30000 + 8000 + 900 + 40 + 5 = $ \displaystyle \overline{{DCXXXV}}MMMCMXLV$

Facts!
1. There is no roman numeral for zero because these numbers were created for trading purposes. They used the word “nulla” instead.
2. Years and dates can be written in roman numerals.
3. Many clocks also use roman numerals to represent the hours.
4. Roman numerals are used to refer to kings or queens, like Henry VIII of England.

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