Roman numerals: reading and building the system — 14–17
Roman numerals are not just decoration on clocks. They are a compact counting system whose symbols and subtraction rules still appear in inscriptions, book chapters and public buildings.
A number made from symbols
Roman numerals write amounts with a small set of letters: I, V, X, L, C, D and M. Usually you add symbols from left to right, but a smaller symbol before a larger one means subtraction, as in IV for four.
Why use this system?
Romans needed a practical way to mark counts, prices, dates and military units before place-value notation became common in Europe. The system works well for labels and monuments, but it is awkward for long calculations because symbols do not show place value.
Reading MCMXLIV
Read MCMXLIV in groups, checking each smaller-before-larger pair. M is 1000, CM is 900, XL is 40 and IV is 4; add them: 1000 + 900 + 40 + 4 = 1944. The grouping prevents you from treating every letter as a simple addition.
The tempting left-to-right sum
A reasonable first attempt is to add every symbol: MCMXLIV becomes 1000 + 100 + 1000 + 10 + 50 + 1 + 5. That gives 2166, because CM, XL and IV are special pairs; whenever a smaller value comes first, subtract it from the next larger one.
Where you still meet them
You still meet Roman numerals on clock faces, in the names of monarchs and popes, in film sequels, book chapters and the numbers of major events. They are useful when a number is acting as a label, not when you need fast arithmetic.
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