Letters are arranged from largest value to smallest and with the value added to the previous ones.
Only powers of ten can be repeated and no letter can be repeated more than 3 times in a row so some numbers must be written using subtraction. This is accomplished by placing the letter of smaller value before the one with a larger value. Only one letter can be subtracted.
Note that "one" is the smallest number because the concept of zero and negative numbers did not exist.
Examples:
100 is not LL (not a power of ten) or XXXXXXXXXX (too many X's repeated).
~ 100 is C
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1510 is not XDM (10 + 500 + 1000) because the largest number value goes first.
~ 1510 is MDX
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800 is not CCM (100 - 100 - 1000) because M is the largest value and C can be repeated up to three times.
~ 800 is DCCC (five hundred plus three hundred)
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45 is not VL because 5 is not a power of ten.
~ 45 is XLV (fifty minus ten plus five)
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140 is not XCL because fifty isn't smaller than ten.
~ 140 is CXL (one hundred and fifty minus ten)
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Or better yet, you can just use this handy online Roman Numeral Converter.
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