A number as the total of its symbols
An old clock face shows I, II, III. Those are numbers too. They are not written the way ours are. How are they written?
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- XXXVII: six symbols.
- Each one's own worth: 10, 10, 10, 5, 1, 1.
- Added up: 37.
- IV breaks the pattern: I before V is 5 − 1 = 4.
Roman numerals — numbers written with letters, as on the clock. They use seven symbols: I, V, X, L, C, D, M.
I is 1, V is 5 and X is 10. L is 50 and C is 100. D is 500 and M is 1,000.
Some pairs have a smaller symbol before a larger one. The smaller symbol is taken away.
Rule: Symbols add. Six pairs take away: IV, IX, XL, XC, CD and CM.
So order matters in these pairs. IX is 10 − 1 = 9. XL is 50 − 10 = 40. XIV is 10 + (5 − 1) = 14. But XVI is 10 + 5 + 1 = 16.
Watch out!
More symbols do not mean a bigger number. VIII is four symbols, worth 8. IX is two symbols, worth 9. The length of the writing is not the size of the number.