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Roman numerals
You can still encounter Roman numerals in everyday life (on buildings, clocks, etc.). This numeral system became widespread throughout Europe during the rule of the Roman Empire and was commonly used until the \latex{ 16 }th century. It is not a positional numeral system, as it uses groups of symbols to express values.
Roman numerals:
\latex{M}
\latex{D}
\latex{C}
\latex{L}
\latex{X}
\latex{V}
\latex{I}
\latex{1}
\latex{5}
\latex{10}
\latex{50}
\latex{100}
\latex{500}
\latex{1,000}
Rules for interpreting Roman numerals:
– Addition: if the values represented by the symbols decrease from left to right, they must be added.
Example: \latex{CCXIII = 213\; (100 + 100 + 10 + 1 + 1 + 1)}
\latex{MDXI = 1,511 \;(1,000 + 500 + 10 + 1)}
– Subraction: if a symbol representing a smaller value precedes a larger one, it must be subtracted.
Example: \latex{CD = 400\; (500 - 100 = 400)}.
Allowed subtractions:
\latex{IV = 4}; \latex{IX = 9}; \latex{XL = 40}; \latex{XC = 90}; \latex{CD = 400}; \latex{CM = 900}.
For example: \latex{CMXLIX = 949}
Allowed subtractions:
\latex{IV = 4}; \latex{IX = 9}; \latex{XL = 40}; \latex{XC = 90}; \latex{CD = 400}; \latex{CM = 900}.
For example: \latex{CMXLIX = 949}
– Multiplication: a line above the numbers means their values must be multiplied by \latex{ 1,000 }.
Example: \latex{\overline{X} = 10,000}; \latex{\overline{XV}= 15,000}; \latex{\overline{D}= 500,000}; \latex{\overline{M} = 1,000,000}
Example: \latex{\overline{X} = 10,000}; \latex{\overline{XV}= 15,000}; \latex{\overline{D}= 500,000}; \latex{\overline{M} = 1,000,000}
Calculating with Roman numerals is difficult. In the Middle Ages, division with Roman numerals was taught at universities. Roman masters used abacuses for practical calculations.
Exercises
{{exercise_number}}. Write down the following numbers using Roman numerals.
a) \latex{ 15 }
b) \latex{ 52 }
c) \latex{ 108 }
d) \latex{ 516 }
e) \latex{ 2,310 }
f) \latex{ 24 }
g) \latex{ 93 }
h) \latex{ 99 }
i) \latex{ 435 }
j) \latex{ 1,742 }
k) \latex{ 2,596 }
l) \latex{ 3,104 }
m) \latex{ 619 }
n) \latex{ 977 }
o) \latex{ 1,555 }
p) \latex{ 12,000 }
q) \latex{ 4,000 }
r) \latex{ 200,000 }
{{exercise_number}}. Write down the following numbers using Arabic numerals.
a) \latex{XVIII}
b) \latex{LII}
c) \latex{LXX}
d) \latex{XLIV}
e) \latex{XXXIII}
f) \latex{DCCL}
g) \latex{DCLXXV}
h) \latex{MCM}
i) \latex{MXI}
j) \latex{MMXXIV}
k) \latex{\overline{XXIV}}
l) \latex{\overline{DLXI}}
{{exercise_number}}. Write down the following numbers using Roman numerals.
- the number greater than \latex{ 195 } by four
- half of \latex{ 1,072 }
- \latex{ 7 } less than four times \latex{ 213 }
- the double of \latex{ 419 }
{{exercise_number}}. Use Roman numerals to write down the following dates.
a) the death of Alexander the Great
b) the discovery of America
c) Moon landing
d) the last Olympic Games
e) dates of birth of your family members
f) the current year
{{exercise_number}}. Which number smaller than \latex{ 100 } contains the most symbols when written with Roman numerals?
{{exercise_number}}. In the exercises below, you can see incorrect equations containing Roman numerals.
a) Add one matchstick to make the equation correct.
b) Move one matchstick to correct the equation.
c) Move two matchsticks to correct the equation.
d) Move one matchstick to correct the equation.
Quiz
What is the smallest number written with Roman numerals that contains all seven symbols exactly once?
