What is the hindu- arabic number for xccmxcix?

Answer 1

Under the accepted convention, XCCMXCIX would be regarded as an invalid numeral.

Roman numerals can be broken down into 13 possible values, which can be combined to form any number from 1 to 3999. The first 7 values are as follows:

I=1

V=5

X=10

L=50

C=100

D=500

M=1000

The accepted convention states that no numeral may be repeated more than 3 times in succession. Thus 3 would be represented by III. However it would be impossible to notate the value 4. Thus the following six combinations are permitted to cater for values that would otherwise be impossible under this convention:

IV=4

IX=9

XL=40

XC=90

CD=400

CM=900

These values are known subtractive pairs. When one small value precedes one large value, we subtract the smaller from the larger. Thus IV is 5-1=4. Although combinations such as IM (1000-1=999) are also possible, the accepted convention does not permit them.

So, breaking the numeral XCCMXCIX down into its component values we get:

xc = 90

cm = 900

xc = 90

ix = 9

While each of these component values are valid by themselves, they are not in descending order. Thus the numeral is considered invalid.

Had each value been in descending order, we would simply add them up. Thus the number could be 1089 (90+900+90+9). However, the accepted convention for 1089 would be written MLXXXIX.

Because the first 90 is followed by a larger value (900), perhaps we are meant to subtract the 90 from the 900? If so, the two 90s cancel each other out and we're left with 909, which would be better written as CMIX.

Even if we ignore the accepted convention, the meaning is ambiguous. So, for both those reasons, the numeral is invalid.