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### Base of Roman Numerals

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Date: 04/07/2001 at 01:32:15
From: Leanne van Cuylenberg
Subject: Base of Roman numeral system

What is the base of the Roman numeral system? I have come to the
conclusion that it is either base 10 or base 5. However, the lack of a
```

```
Date: 04/07/2001 at 23:14:41
From: Doctor Peterson
Subject: Re: Base of Roman numeral system

Hi, Leanne.

The Roman system is fundamentally base ten, because it represents the
state of an abacus (which has ones and fives for each base ten digit),
and agrees with their base ten names for numbers (using hundreds,
thousands, and so on). It is not a _positional_ system (which accounts
for the lack of a zero) but that does not mean it is not a _base ten_
system. I've somewhere heard it described as a sort of mix of bases
five and ten, but I don't think that's really significant. Essentially
it is base ten, with combinations of symbols used for each digit.

You will want to check our FAQ on Roman Numerals, which explains
something of the meaning of the system:

http://mathforum.org/dr.math/faq/faq.roman.html

- Doctor Peterson, The Math Forum
http://mathforum.org/dr.math/
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High School Number Theory
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