Ask A Scientist Mathematics Archive

Author:      kantars
In roman numerals there is no zero.  
1) How did they represent zero with a symbol in roman times?
2) How did the Romans write the number 5,000 in symbols?
3) What date was it when George Washington was born?

Response #:  1 of 3
Author:      asmith
Sorry, the date Washington was born is a History question, not math. . .
There really was not the concept of zero in any number system until it was
invented in various different places, I think around 500-1000 C.E.  Until
then, numbers were used in ways that were for the most part independent of
where the numbers actually were in the expression.  So, like the Romans,
they had to come up with a different symbol for successively larger numbers,
rather than carrying lots of I's around.  But still counting was sort of
like adding up poker chips - add up the number of 1's, add on the number of
10's, then the number of 100's etc.  The Roman system was a little more
advanced (maybe) in having a more systematic system, involving 5's also, and
numbers were always put together in the same order, with the big counters 
(M etc.) coming first.  But they never figured out zero, and actually they
did not really need it, since the counting system was complete without it. 
But addition and especially multiplication becomes an awful lot easier with
the Arabic place-holding system we use now, and zero is essential to it.

I have never seen the Roman numeral for 5000, so I am not sure there ever
was one.  They may have just used 5 M's.  That is certainly what they did
for anything larger than the largest number there was an assigned letter
for.

Response #:  2 of 3
Author:      rcwinther
According to the Encyclopedia Americana, the Romans used a symbol that looks
like a backward "C" (which was called an apostrophus) to represent large
numbers.  (I will use a ">" for this symbol in what follows.)  For example,
before they used "M" (which probably came from their word "mille," meaning a
thousand) they used "CI>" for 1000 and "I>" (which eventually became "D")
for 500.  Then CCI>> meant 10,000 and CCCI>>> meant 100,000, and so on; I>>
meant 5000, I>>> meant 50,000, etc. Sometimes (especially in later Latin) a


bar, called a vinculum, was placed over a symbol to denote multiplication by
1000; so V with a bar over it meant 5000, etc.  There was no symbol for
zero, but because the Roman notation does not use place holders there really
was not a need: one simply used a word like "nihil" (meaning "nothing") or
"nullus" (meaning "none").

Response #:  3 of 3
Author:      rcwinther
Regarding Washington's birthday:
 sure it is history, but we can sneak in a little science anyway.  If you
look in some encyclopedias, e.g., Britannica, you will see that George
Washington was born on February 22, 1732 (New Style) or February 11 (Old
Style).  Worse, in the Old Style calendar, New Year's Day was March 25, so
for example the day after March 24, 1700 was March 25, 1701.  Thus, George
Washington was born on February 11, 1731 (O.S.) or February 22, 1732 (N.S.).

"Old Style" refers to the Julian calendar, imposed on the Roman Empire by
Julius Caesar and retained thereafter in Europe.  Its main claim to fame was
the use of a leap year every 4 years to take into account the fact that the
year is not 365 days, but 365 1/4 days.  Well, almost.  A year is about 11
1/4 minutes shy of 365 1/4 days, and over the centuries this error accumu-
lated.  In 1582 Pope Gregory XIII decreed that the day following October 4,
1582 would be October 15, 1582, and he modified the leap year rule that a
century year (e.g., 1900) would NOT be a leap year unless it was also
divisible by 400 (so 2000 will be a leap year).  With this scheme, addition-
al tinkering will not be necessary for many centuries.  However, England and
her colonies did not adopt the Gregorian calendar until 1752 (the same Act
that adopted the Gregorian calendar also moved New Year's Day to its present
January 1.)