Roman Numbers - Conversion to decimal number I have read that if a smaller number is to the left of a larger number means that the smaller number has to be subtracted from the larger number.
Ok I can understand quickly for below Roman Numbers :
IX = X - I = 10 - 1 = 9

But I have difficulty in understanding Roman Numbers that have odd Roman Numerals - say :
XIX 

So if we go from Left to right we get
XIX = 10 + 1 + 10 = 21

But if we go from right to left we get
XIX = 10 + 10 - 1 = 19

So which direction we should consider before applying the rule of smaller followed by bigger Roman Numerals - left to right or right to left? 
 A: When you are reading Roman numerals, start from the left-most character. Read rightward until the value of the character increases. Then, section those two characters off, and repeat.
That sounds really complicated, and I wrote it somewhat poorly, so here are some examples.
In $XIX$, we start with the left $X$ which is $10$. Then we move to the $I$ which is $1$. We decreased from $10$ to $1$, so we'll move on. Then we get to the right $X$ which is $10$. We increased from $1$ to $10$, so we need to section off the $IX$. It would look like this:
$$XIX = X + IX = 10 + 9 = 19$$
Here's a more complicated example:
$$MCMXXIX = M + CM + XX + IX = 1000 + 900 + 20 + 9 = 1929$$
Here we had to section off the $CM$ since we increased in value from $C$ to the second $M$. We had to section off the $IX$ since we increased in value from the $I$ to the last $X$.
One last really complicated example:
$$MMCDXLIV = MM + CD + XL + IV = 2000 + 400 + 40 + 4 = 2444$$
A: You can apply the following logics: 


*

*the units are denoted I, II, III, IV, V, VI, VII, VIII$^*$, IX; the tenths are denoted X, XX, XXX, XL, L, LX, LXX, LXXX, XC; the hundredths C, CC, CCC, CD, D, DC, DCC, DCCC, CM; the thousands, M, MM, MMM.

*numbers are written in thousands, hundredths, tenths and units from left to right.

*no other pattern is allowed.


The Roman Empire wasn't designed to last longer than until 3999 AD :)

$^*$Sometimes IIX is used for VIII.
A: XIX is read left to right, the "I" is always applied to the final X.
XIX = X + IX = 10 + 9
XXI = X + XI = 10 + 11
A: When reading roman numerals, I prefer to think in the following way:
Read from left to right, and if at any point the value of a character decreases, put a comma between the decrease.  Then, add each block together.
MCMXCVI $\mapsto$ M,CM,XC,V,I $\mapsto$ $1000+900+90+5+1=1996$
MDCCCLXXIV $\mapsto$ M,D,CCC,L,XX,IV $\mapsto$ $1000+500+300+50+20+4=1874$
MCMXCIX $\mapsto$ M,CM,XC,IX $\mapsto$ $1000+900+90+9 = 1999$
Note that 1999 was not written as IMM or MIM.  Converting from arabic numbers to roman numerals, one only uses powers of ten one apart to denote subtraction.
A: I have designed following algorithm to convert roman to decimal.


*

*Let Roman String be ......

*Replace string contents of length = 4 with appropriate content


*

*Length = 4, Roman numerals are VIII = 8


*Replace string contents of length = 3 with appropriate content


*

*Length = 3, Roman numerals are MMM = 3000, XXX = 30, VII = 7, III = 3


*Replace string contents of length = 2 with appropriate content


*

*Length = 2, Roman numerals are MM = 2000, XX = 20, XI = 11, IX = 9, VI = 6, IV = 4, II = 2


*Once this is done, then follow below rules:


*

*Subtract digits from each other


*

*I can be subtracted (absolute) from V or X

*X can be subtracted (absolute) from L or C

*C can be subtracted (absolute) from D or M


*Finally there will be a bunch of digits. Add all of them to get the answer


A: To avoid confusion , the only pairs of Roman numerals that follow the "subtraction" rule are IV, IX, XL, XC, CD, CM. So if your shirt size followed Roman numerals ( which it does not) L would be 50, XL=50-10=40 and XXL = 10+40=50 . Therefore L would be equal to XXL size in Roman numerals !! Coming onto XIX , this equals 19 . Here we must keep in mind the other rules of Roman numerals also and not just addition subtraction. 20 as a digit as a whole is represented as XX and therefore 21 would be XXI. In XIX reading from left to right take IX as a complete digit ie 9 and therefor XIX =19
