>For example can you think of the rules to multiply XVIV with XXV or can you quickly calculate what the result of that will be without translating to a decimal

>For example can you think of the rules to multiply XVIV with XXV or can you quickly calculate what the result of that will be without translating to a decimal number system ? Exactly! Well, very likely the Romans had some tricks to do that (and besides very likely they did use an abacus), the fact that it appears difficult to us (having been immersed in positional notation) does not mean much. This algorithm (making use of halving and doubling) doesn't look so bad: http://rbutterworth.nfshost.com/Tables/romanmult http://rbutterworth.nfshost.com/Tables/romanmult and it can be used also with our "positional" numbers. http://www.phy6.org/outreach/edu/roman.htm http://www.phy6.org/outreach/edu/roman.htm The abacus (the Chinese "suanpan" or a derivative of it, as it is still used in some eastern countries) is - in the hands of someone used to it - very fast, I have seen people be on par or outperform a "westerner" trying to do the same operation on a pocket calculator, I wouldn't be surprised if the Romans abacus was as fast as that: https://en.wikipedia.org/wiki/Roman_abacus https://en.wikipedia.org/wiki/Roman_abacus the base as decimal (or actually bi-quinary) is the same.