HFCC Math Lab
NAT – 07
Converting Roman Numerals to Arabic Numerals
Face value of Roman numerals
Some often used characters in Roman numerals and their face value listed below:
I
One
V
Five
V
Five Thousand
X
Ten
X
Ten Thousand
L
Fifty
L
Fifty Thousand
C
One Hundred
C
One Hundred Thousand
D
Five Hundred
D
Five Hundred Thousand
M
One Thousand
M
One Million
Using these characters you can write any positive number from 1 up to 4,999,999. To represent higher
numbers you introduce characters similar to one on the second column with more bars. For example, five
million is represented by the character V .
Place value of Roman numerals
Every roman numeral is written as a string of characters. To find the Arabic numeral corresponding to the
given Roman numeral, write down the face value of every character in the given string and then either add or
subtract the face value.
To determine when to add the value and when to subtract the value, use the following rules:
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•
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Start converting Roman numerals to Arabic numerals from left to right.
If the face value of a character is smaller than the character following it, subtract the first character.
Otherwise add the first character.
Always add the last character in the string.
Example 1: Roman numeral XI translates as +10 +1 = +11 in Arabic numerals. Since the face value
of X is higher than face value of I, we add the face value of X to the face value of the last character I
Example 2: Roman numeral IX translates as –1 +10 = +9 in Arabic numerals. Since the face value
of I is smaller than face value of X, we subtract the face value of I from the face value of the last
character X.
Revised 5/11
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Sample Problems:
Write the Arabic numeral corresponding to the given Roman numerals:
Problem 1: V
Solution: + 5 = 5
Problem 2: VIII
Solution: +5 + 1 + 1 + 1 = 8
Problem 3: XVI
Solution: +10 + 5 + 1 = 16
Problem 4: IV
Solution: –1 + 5 = 4
(Remark: Since the face value of the character following I is smaller than the face value of V we subtract the
face value of I)
Problem 5: LXI
Solution: +50 + 10 +1 = 61
Problem 6: XLI
Solution: –10 + 50 + 1 = 41
Problem 7: DCLXVI
Solution: +500 + 100 + 50 + 10 + 5 + 1 = 666
Problem 8: CDXLIV
Solution: –100 +500 – 10 + 50 – 1 + 5 = 444
Problem 9: M M X LX
Solution: +1,000,000 + 1,000,000 – 10,000 + 50,000 + 10 = 2,040,010
Problem 10: MMMCMLXXVII
Solution: +1000 + 1000 + 1000 – 100 + 1000 + 50 + 10 + 10 + 5 + 1 +1 = 3977
Revised 5/11
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Exercise Problems:
Write the Arabic numeral corresponding to the given Roman numerals
1. MM
2. CCCXXXIII
3. V DLV
4. CDXLIV
5. LXVII
6. XLVIII
7. XXIX
8. CCCXLV
9. XCVI
10. CCXXXIV
11. DCLVI
12. MCXLVIII
13. MMCCCLXVII
14. DXLV MCMLXXIII
15. MMMCDXCIX
Revised 5/11
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Solutions to Exercise Problems:
1. 2, 000, 000
2. 333
3. 5555
4. 444
5. 67
6. 48
7. 29
8. 345
9. 96
10. 234
11. 656
12. 1148
13. 2367
14. 546,973
15. 3499
Useful Websites:
http://wolframalpha.com
-This website will help you convert any Arabic numerals to Roman numerals. In the space provided enter
“21 in Roman Numeral” to get the Roman numeral equivalent value XXI
http://www.novaroma.org/via_romana/numbers.html
- Coverts Roman Numerals to Arabic and vice versa. It also gives strategies for converting Roman Numerals
to Arabic Numerals.
Revised 5/11
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