What base is Roman Numerals? What is the base for Roman Numerals? It starts off with unary then goes back and forth between multiples of 5 and 10.
 A: I disagree with Henning's and J.M.'s identification of positional systems and systems with a base. There are examples of non-positional systems with a single base (10 in both cases): Egyptian numerals and Chinese numerals. The first footnote in the Wikipedia article on Roman numerals calls them "a decimal system in which the number 5 is an auxiliary base". 
A: Since it is not a positional system, it does not really make sense to speak of a unique "base" for Roman numerals, mathematically. One could describe them as "mixed base 5-10" (most commonly) or even "mixed base 2-5", but neither of those are formal descriptions.
A: The concept of a numeral base is a characteristic radix numeral systems.  This includes the familiar systems such as base 10 and base 2, but also includes base -2 (negative), base 2i (imaginary), base i-1 (complex) or even base e (transcendental) for that matter.
The Roman numeral system is not a radix system and therefore has no corresponding base characteristic.
There are many online references that discuss various aspects of this.  Here is one.
