Section 2.5 Roman Numerals
The Romans used a special method of showing numbers, based on the following symbols: These
7 symbols are the only Roman numerals. We can’t write 0, negative numbers or fractions using
Roman numerals.
1
5
10
50
100
500
1000
I
V
X
L
C
D
M
Numbers greater than 4,000 are formed by placing a dash over the symbol, meaning "times
1,000", but these are not commonly used, and we won’t study them:
5,000
_
V
10,000 50,000 100,000 500,000 1,000,000
_
_
_
_
_
X
L
C
D
M
We never write more than 3 of the same symbol in a row. Notice how we write 4 and 9 and 40
and 90 in the table below. Writing a “larger” number to the left of a smaller number tells you to
subtract.
1
2
3
4
5
6
7
8
9
I
II
III
IV
V
VI
VII
VIII
IX
10
20
30
40
50
60
70
80
90
X
XX
XXX XL
L
LX
LXX
LXXX XC
100
200
300
400
500
600
700
800
C
CC
CCC
CD
D
DC
DCC DCCC CM
900
Now let’s try to convert Roman numerals into common numbers. These common numbers are
called Hindu-Arabic numbers.
Example: Convert XIV to Hindu-Arabic numbers.
Step 1: We need to know which number each letter stands for.
I=1
V=5
X = 10
Step 2: Locate the largest symbol within the number. This should be the first or second number.
XIV
In our problem the X is the symbol with the largest value.
If there is no symbol before the symbol with the largest value just add the value of this symbol to
our total.
In our case there is no symbol preceding the X, so I will add 10 to my total.
Total so far: 10
Step 3: Remove the X from our number and repeat the process.
Here is what is left when you remove the X from our number.
IV
Look for the largest number in our reduced number.
In our problem the V is the symbol with the largest value.
I can’t just add the value of a V which is 5 to our total.
If a number precedes the largest number, I must subtract the value of the symbol before it from
its value and add that number to the total.
IV = 5 – 1 = 4
Add this number to our total.
Total so far: 10 + 4
We have use up all of the Roman numerals so I can just finish adding and write my answer.
Answer: XIV = 14
Example: Convert CXCVII to Hindu-Arabic numbers.
I will solve this problem in a table. I will be doing the exact same technique. I think it will be
easier to follow in a table. You might not think this seems easier at first. But I think you will
after watching me work a few of these on my video.
Steps to fill in the table:
1) Write the number in the upper left corner.
2) Beneath the number write the symbol with largest value in the number. This will be the first
or second number. Include both symbols if the largest value is second.
3) Write the value of that symbol beneath the symbol.
4) Remove the symbol or symbols that were used when creating a column and write the
remaining symbols in the top row of the next column.
5) Repeat steps 1 – 4 until all symbols have been used.
6) Add the values in the bottom row.
First step: Write the number in the upper left corner. C is the symbol with the largest value. I
will write it beneath the number. Write the value of C beneath the C. Remove the C from the
number and write what remains in the top of the next column.
Remaining
number
Largest
symbol
value
CXCVII
XCVII
C
100
Second step: C is the symbol with the largest value. I will write XC beneath the number. Write
the value of XC beneath the XC. Remove the XC from the number and write what remains (VII)
in the top of the next column.
Remaining
number
Largest
symbol
value
CXCVII
XCVII
C
XC
100
90
VII
Third step: V is the symbol with the largest value. I will write V beneath the number. Write the
value of V beneath the V. Remove the V from the number and write what remains (II) in the top
of the next column.
Remaining
number
Largest
symbol
value
CXCVII
XCVII
VII
C
XC
V
100
90
5
II
Fourth step: I is the symbol with the largest value. I will write I beneath the number. Write the
value of I beneath the I. Remove the I from the number and write what remains (I) in the top of
the next column.
Remaining
number
Largest
symbol
value
CXCVII
XCVII
VII
II
C
XC
V
I
100
90
5
1
I
Fifth step: I is the symbol with the largest value. I will write I beneath the number. Write the
value of I beneath the I. Remove the I from the number and write what remains (I) in the top of
the next column.
Remaining
number
Largest
symbol
value
CXCVII
XCVII
VII
II
I
C
XC
V
I
I
100
90
5
1
1
Nothing
left
Last step: I have used up all of the symbols. I just add the numbers in the bottom row to get my
answer.
Answer: 100 + 90 + 5 + 1 + = 197
Example: Write MCMLXIV as a Hindu Arabic numeral.
I will do this as a single table. This may be hard to follow. I won’t show any explanation. I will
explain this table in my video.
Remaining
number
Largest
symbol
Value
MCMLXIV CMLXIV
LXIV
XIV
IV
M
CM
L
X
IV
1000
900
50
10
4
None left
Answer: 1000 + 900 + 50 + 10 + 4 = 1964
Homework: #1-28 Write as a Hindu Arabic numeral.
1) CCXLII
2) DXLVI
3) CDXLVII
4) CDXXXIV
5) LXXXVI
6) LXXVII
7) CXXIII
8) CXXXI
9) XLIX
10) XLIV
11) DCXVI
12) DCCLXVI
13) XXXIV
14) XXXIX
15) XCIX
16) XCIV
17) MCMXXX
18) MCMXCIII
19) MMCMIV
20) MMCMXCV
21) MMXIV
22) MMXIX
23) CMXCVII
24) CMXLVII
25) DCXLVII
26) DCCXLIX
27) CDLVI
28) CDXLVII
Now we need to go “backwards”.
These tables will help us go backwards.
“ONES 1 – 9”
Roman I
numeral
Hindu- 1
Arabic
II
III
IV
V
VI
VII
VIII
IX
2
3
4
5
6
7
8
9
XX
XXX XL
L
LX
LXX
LXXX XC
20
30
40
50
60
70
80
TENS 10 – 90”
Roman X
numeral
Hindu- 10
Arabic
90
HUNDREDS 100 – 900”
Roman C
numeral
Hindu- 100
Arabic
CC
CCC
CD
D
DC
DCC
DCCC CM
200
300
400
500
600
700
800
900
THOUSANDS 1000 – 3000 (We won’t study Roman Numerals over 4,000)
Roman M
MM MMM
numeral
Hindu- 1000 2000 3000
Arabic
Example: Write 278 as a Roman numeral
Break the number up into hundreds, tens and ones.
278 = 200 + 70 + 8
Attach a Roman numeral to each. Use the table to get the values.
200 = CC
70 = LXX
8 = VIII
Answer: CCLXXVIII
Example: Write 2419 as a Roman numeral.
Break the number up into thousands, hundreds, tens and ones.
2419 = 2000 + 400 +10 + 9
Attach a Roman numeral to each. Use the table to get the values.
2000 = MM
400 = CD
10 = X
9 = IX
Answer: MMCDXIX
Homework: # 29 – 60 Write as a Roman numeral.
29) 53
30) 57
31) 18
32) 17
33) 125
34) 131
35) 316
36) 722
37) 19
38) 29
39) 34
40) 24
41) 49
42) 44
43) 47
44) 48
45) 95
46) 98
47) 432
48) 446
49) 951
50) 957
51) 948
52) 941
53) 1950
54) 1973
55) 1994
56) 1999
57) 2016
58) 2019
59) 2024
60) 2043
Answers:
1) 242 3) 447 5) 86 7) 123 9) 49 11) 616 13) 34 15) 99
17) 1930 19) 2904 21) 2014 23) 997 25) 647 27) 456
29) LIII 31) XVIII 33) CXXV 35) CCCXVI 37) XIX
39) XXXIV 41) XLIX 43) XLVII 45) XCV 47) CDXXXII
49) CMLI 51) CMXLVIII 53) MCML 55) MCMXCIV
57) MMXVI 59) MMXXIV