One number, several ways of writing it
A date plate on an old building reads MCMXC. That is 1990. One year, two ways of writing.
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Step 1 of 4
- 2024 as MMXXIV: 6 symbols.
- 2024 as digits: 4 digits.
- 12345678, digit by digit.
- Grouped for reading: 1,23,45,678.
A symbol fits when its worth is at most what is left.
Rule: Take the largest symbol or pair that fits. Write it. Repeat.
Write 1990. M fits, and 990 is left. CM fits, and 90 is left. XC fits, and 0 is left. So 1990 is MCMXC.
The largest symbol is M, worth 1,000. A big number needs many copies of it. The number 1,23,45,678 has 12,345 thousands and 678 more. So it needs 12,345 copies of M, then DCLXXVIII. DCLXXVIII has 9 symbols, so that is 12,345 + 9 = 12,354 symbols. Our digits write it with only eight digits.