Two Types of numbers
         Two Types of numbers
   Arabic numbers 
    Arabic numbers 
       The numbers we normally use
       The numbers we normally use
       1,2,3,4,,,,,,,,
       1,2,3,4,,,,,,,,
   Roman Numbers
    Roman Numbers
       Invented by the romans and still used today 
       Invented by the romans and still used today 
       I, V, X, L, C, D, M
       I, V, X, L, C, D, M
     Hx of Roman numerals
     Hx of Roman numerals
  Romans strictly represented units as 
  Romans strictly represented units as 
  separate items in their numbers. 
  separate items in their numbers. 
  the numerals represented numbers as they 
  the numerals represented numbers as they 
  were depicted on an abacus - a calculating 
  were depicted on an abacus - a calculating 
  machine using pebbles or beads which were 
  machine using pebbles or beads which were 
  arranged from right to left in columns of 
  arranged from right to left in columns of 
  units, tens, hundreds, thousands etc. 
  units, tens, hundreds, thousands etc. 
         Continued……
          Continued……
   That means that 99 could be represented as 
   That means that 99 could be represented as 
   XCIX - 90+9 but never as IC. 
   XCIX - 90+9 but never as IC. 
      XC = 10 subtracted from 100 = 90
      XC = 10 subtracted from 100 = 90
      IX = 1 subtracted from 10 = 9 
      IX = 1 subtracted from 10 = 9 
      90 + 9 = 99
      90 + 9 = 99
   999 cannot be IM 
   999 cannot be IM 
      IM is not legal
      IM is not legal
      999 = CMXCIX 
      999 = CMXCIX 
       CM = 100 from 1000=900, XC = 10 subtracted from 
       CM = 100 from 1000=900, XC = 10 subtracted from 
      100 = 90 and IX = 1 subtracted from 10 = 9 
      100 = 90 and IX = 1 subtracted from 10 = 9 
       Therefore 900 + 90 + 9 = 999 
       Therefore 900 + 90 + 9 = 999 
       Roman Numerals
       Roman Numerals
       You must Learn
        You must Learn
  I = 1
  I = 1
  V = 5
  V = 5
  X = 10
  X = 10
  L =50
  L =50
  C =100
  C =100
  D = 500
  D = 500
  M = 1000
  M = 1000
      Roman Numeral Rules 
      Roman Numeral Rules 
   You can’t add more than 3 of the same letters at 
   You can’t add more than 3 of the same letters at 
   one time. 
   one time. 
   – Ex: 4 is IV not IIII
     Ex: 4 is IV not IIII
   use the biggest numeral possible at each stage  
   use the biggest numeral possible at each stage  
   – Ex: 15 XV not VVV or XIIIII. 
     Ex: 15 XV not VVV or XIIIII. 
   A smaller value letter to the left of a larger value 
   A smaller value letter to the left of a larger value 
   one is subtracted
   one is subtracted
   – Ex: 34 is XXXIV not XXXIIII
     Ex: 34 is XXXIV not XXXIIII