The Base of Roman NumeralsDate: 02/19/2004 at 03:06:50 From: Emma Subject: Roman Numerals What base does the Roman Numeral system use? It appears to have two bases. Date: 02/19/2004 at 12:07:28 From: Doctor Peterson Subject: Re: Roman Numerals Hi, Emma. This question is discussed here: Base of Roman Numerals http://mathforum.org/library/drmath/view/52587.html The system is essentially base 10, since a numeral can always be broken into parts for each power of ten: M CM LX VII 1 9 6 7 It can be described as a combination of bases 2 and 5, since the values of the symbols involved are either 2 or 5 times the value of the previous symbol: I V X L C D M 1 5 10 50 100 500 1000 *5 *2 *5 *2 *5 *2 But that doesn't really make it base 2 or base 5, and since it is not a place-value system, the role of 2 and 5 is not very significant. No powers of 2 or 5 are involved, only powers of 10 times 1 or 5. That's why I prefer to think of it as a modified base-10 system influenced by base 5. It's interesting, though, that the abacus (which IS a place-value system) uses the same trick of splitting each decimal digit into two parts, one base 2 (two beads representing fives, only one of which is actually needed) and one base 5 (five beads representing ones). Roman numerals, apart from subtractive notation (as in IV for 4), represent well the state of such an abacus, with the digits corresponding to each power of ten showing how many 1's and how many 5's there are in that "digit". If you have any further questions, feel free to write back. - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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