A Story of Numbers · Lesson 3 of 8
The Roman Numerals
“Understand Roman landmark numbers, representation and arithmetic limitations.”
• Read and write common Roman numerals. • Explain the idea of landmark numbers. • Represent numbers as sums of Roman landmark values. • Compare the efficiency of Roman numerals with simpler tally systems. • Explain why Roman numerals make arithmetic difficult.
IV. The Roman Numerals
Roman numerals improve on a system that uses only one group size. Instead of relying on one repeated unit, they use several important reference values such as 1, 5, 10, 50, 100, 500 and 1000.
A recognisable reference number used as an anchor for representing and working with other numbers.
To represent a number, break it into landmark values. For 27, use as many 10s as possible, then 5s, then 1s.
Problem
Write 27 in Roman numerals.
- 1.27 = 10 + 10 + 5 + 1 + 1.
- 2.10 is X, 5 is V and 1 is I.
- 3.So 27 = XXVII.
Roman notation also uses some subtractive forms. IV represents one less than 5, so it means 4. XL represents ten less than 50, so it means 40. Historical use was not always perfectly consistent.
Problem
Write 1222 in Roman numerals.
- 1.1222 = 1000 + 100 + 100 + 10 + 10 + 1 + 1.
- 2.Use M for 1000, C for 100, X for 10 and I for 1.
- 3.So 1222 = MCCXXII.
This system is far more compact than making one mark for every object. A single M can represent 1000. But compact representation does not automatically mean easy arithmetic.
Addition can be done by collecting Roman symbols and regrouping them into larger landmarks, but the regrouping sizes are not uniform. Multiplication and division are even more difficult because Roman landmark values are not generated by one fixed multiplication rule.
In XXVII, each X is still worth 10. Its value does not change because of position.
Quiz
Which Roman numeral represents 50?
Why are Roman numerals more efficient than pure tally marks?
What is XXVII?
Which statement about Roman numerals is true?
Why is multiplication difficult in Roman numerals?
Practice Problems
- Write 37 and 84 in Roman numerals.
- Write 302, 715 and 1222 in Roman numerals.
- Expand MMCCCLXII as a sum of landmark values and determine the number it represents.
- Explain how landmark numbers make Roman numerals more compact than a one-mark-per-object system.
- Compare Roman numeral arithmetic with Hindu numeral arithmetic. Identify one representation advantage and one calculation disadvantage.
Key Takeaways
• Roman numerals use several landmark numbers rather than one repeated group size. • I, V, X, L, C, D and M represent 1, 5, 10, 50, 100, 500 and 1000. • Numbers can be built by combining landmark values. • Roman notation is much more compact than tally marks. • Roman symbols have fixed values rather than place values. • Arithmetic is difficult because the landmarks are not successive powers of one fixed base.