Yes exactly, 40 is 10 50! In each place value (e.g. units, tens, hundreds), there's a symbol for 1, a symbol for 5, and a symbol for 10. You place the symbol for 1 on the left of a bigger symbol to subtract, and on the right to add.
In the one's place: 1=I, 5=V, and 10=X, so:
To get to 3 (three), you just have three 1s: III
To get to 8 (eight), you go up from V by 3: VIII
(don't ask me why they don't do IIX even though it's shorter, I guess you can only subtract one time in each place value)
To get to 9 (nine), you go down one from 10: IX
In the ten's place 1=X, 5=L, 10=C (10, 50, 100), so:
To get to 3 (thirty), you go up three from nothing: XXX
To get to 7 (seventy), you go up two from L: LXX
To get to 9 (ninety), you go down 1 from C: XC
Similarly, the hundreds place has C, D, and M, and so on.
So to write a year, like 1983, you write 1000 900 80 3. That is, M CM LXXX III. And indeed, 1983 is MCMLXXXIII.
Do note I don't think this is how roman numerals are usually taught, and I didn't learn them like this either. This is just how I think about them currently.
Programmatically, I would start with an empty string, and peel off the digits one at a time by doing digit=n%10 and n=n/10. Then, I would convert the digit to the roman numeral form and prepend it to the string. As you said, you could convert this with a hardcoded table (which would probably be faster), or you could try to be fancy about it.
(That could be something like turning 7ā5 1 1, then replacing the numbers by the roman numerals based on what place value (iteration of the digit-peeling loop) you're in. So in the first loop, V would replace 5 and I would replace 1 to get VII; in the second it would be L and X respectively to get LXX; and so on. That's needlessly complicated though, I think)
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