2.1.6 Roman Numerals

The following are the roman numerals commonly tested on the exam:

SymbolValue
I1
V5
X10
L50
C100
D500
M1000

Knowing the above table and also the fact that you arrange the numerals in order from greatest to least (M → I) with the exception of one rule: you can’t put four of the same numerals consecutively.

For example, to express 42 in roman numerals it would not be 42 = XXXXII, it would be 42 = XLII. To circumvent the problem of putting four of the same numerals consecutively, you use a method of “subtraction.” Anytime a numeral of lesser value is placed in front of a numeral of greater value, you subtract from the larger numeral the small numeral. So in our case 40 is represented by XL = 50 − 10 = 40.

When converting numbers, it is best to think of the number as a sum of ones, tens, hundreds, etc… units). A good example of what I mean is to express 199 in roman numerals. The way you want to look at it is 199 = 100 + 90 + 9 then express each one as a roman numeral. So 100 = C, 90 = XC, and 9 = IX, so 199 = CXCIX.

Problem Set 2.1.6

MMXLII =
XLIV =
MMIII =
CXCIX =
MDCLXVI =
CDXLIV =
CCLXXVII =
MCDLIX =
CMXCIX =
MMCCXXII =
CXI - CC =
MD + DC =
CM + XC + IX =
DC - LX - VI =
XIII + MMIV =
MIII + MIV =
MC + DL + XIV =
MCXI + DLV =
MMV - DCXLI =
MMLIX - LIII =
MCXI - DLV =
CMIX - CDIV =
MDXLV - XV =
DCII ÷ IX =
CCCLXXIV ÷ XI =
CDI × V =
CCLXXX ÷ XIV =
MMV ÷ V =
XXVII × CXI =
MI × XI =
MMVII × XXV =
MCCLX ÷ XV =
MMVI × XI =
CDIV ÷ XL =