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Unit A6 Section 1
Roman Numerals

The number system that we use in daily life is the base 10 (Arabic) system.

Roman numerals, the numeric system used in ancient Rome, uses letters from the Latin alphabet in an equivalent system of representing numbers.

In the Roman system we use

I for 1
V for 5
X for 10
L for 50
C for 100
D for 500
M for 1000

The values of consecutive letters are ADDED unless a letter with a lower value appears in front of a letter with a higher value. When this is the case, the lower value letter is SUBTRACTED from the higher value, as shown in the following examples.

Examples of the effects of the order in which letters are placed:

VII = 5 + 1 + 1 = 7
XXV = 10 + 10 + 5 = 25
IV = 5 − 1 = 4
IC = 100 − 1 = 99
VL = 50 − 5 = 45

Worked Examples

1

Complete these number lines using Roman numerals.

(a)
(b)
2

Convert the following Roman numerals to base 10.

(a)
II = 1 + 1 = 2
(b)
IX = 10 − 1 = 9
(c)
DI = 500 + 1 = 501
(d)
LIX = 50 + (10 − 1) = 59
3

Convert the following base 10 numbers to Roman numerals.

(a)
14 = 10 + 4 = 10 + (5 − 1) = XIV
(b)
84 = 50 + 30 + 4 = 50 + 30 + (5 − 1) = LXXXIV
(c)
27 = 20 + 5 + 2 = XXVII
(d)
1010 = 1000 + 10 = MX

Exercises

Convert the following Roman numerals to base 10.

(a)
VIII
(b)
CD
(c)
DVI
(d)
CDXC

Convert the following base 10 numbers to Roman numerals.

(a)
6
(b)
109
(c)
56
(d)
1499

Complete the number line using Roman numerals.

Change the Roman numerals to base 10 numbers.

(a)
(i)
DIX
(ii)
MCMXLV
(iii)
CMIV
(iv)
CDXVI
(v)
MCXI
(vi)
CMXCIX
(b)
(i)

List the numbers in (a) above in decreasing order.

         
(ii)

Divide the second number in your list by 11 and write the answer in Roman numerals.

Above the entrance to a church there is a Roman number

MDCCXCI

(a)

When do you think the church was built?

The crypt was built 153 years before the main church.
(b)

What Roman number is carved in the wall of the crypt?

Which Roman numeral can written instead of the shapes to make the statements true?

Give your answers in Roman numerals.

(a)
CDLXXIX < < CDLXXXIII

:

(b)
CMXCVIII < < MIV

:

Continue the sequences, giving the next 3 terms, using Roman numerals.

(a)
XLVII,   LXVII,   LXXXVII,   ,   ,  
(b)
CMI,   DCCCI,   DCCI,   ,   ,  

The sum of any two adjacent numbers is the number directly above them. Fill in the missing numbers.

(a)
(b)