I can't tell you much about the numerological implications of the number and the interpretation of Johannes, but I'm going to say something about Roman numbers that might be helpful:

Roman numerals don't use positional notation, but they still represent base-10 - there are symbols for the decimal powers: I, X, C, CD (= later M) and so on, combined with symbols for half of them: V, L, D. Fun fact: the symbols for the half of the decimal powers are simply the letters chopped in half: X > V; C > L; CD > D. DCLXVI (or ΧΞϚ in Greek numerals) when spoken or written out it is sexcentos sexaginta sex, hexakosioi hexekonta hex in Ancient Greek, (sixhundred sixty six), so it loses none of that remarkableness and in fact has much to do with the number 6. In fact, it allows additional interpretations when written that way, since numbers are written with the same symbols as names are - Johannes remarks that:

ἀριθμὸς γὰρ ἀνθρώπου ἐστί, καὶ ὁ ἀριθμὸς αὐτοῦ ἑξακόσιοι ἑξήκοντα ἕξ

"for it is the number of a human, and his number is sixhundredsixtysix", one interpretation being that you can reconstruct it into the name of a human.

See also /u/talondearg's answer on Greek numbers and the numerological implications.

To build and complement two quite good answers:

The text this is derived from is Revelation 13:18, I quote below the Greek and an English translation: 18 ὧδε ἡ σοφία ἐστίν· ὁ ἔχων νοῦν ψηφισάτω τὸν ἀριθμὸν τοῦ θηρίου, ἀριθμὸς γὰρ ἀνθρώπου ἐστίν· καὶ ὁ ἀριθμὸς αὐτοῦ ἑξακόσιοι ἑξήκοντα ἕξ.

Here is wisdom: let the one that has understanding calculate the number of the beast, for is a human number: and its number is 666.

Greek numbers can be represented by words, as in this edition, but it was more common to use letters to symbolise them. P47 reads χ̅ξ̅ϛ̅ whereas a manuscript such as P115 reads χ̅ι̅ϛ̅. The former works out to 666, the latter to 616. Overall the textual tradition for 666 is relatively stronger than that for 616. Most attempts to explain the number centre on three methods: (1) That it is purely symbolic, and so should be taken just ‘as is’; (2) that it is chronological, indicating some kind of duration of the beast’s reign, (3) some use of Gematria, in which the correspondence of letters and numbers is used to represent words by the sum of their numerical equivalents.

In the case of 666, the most common attempt is to identify 666 with Nero. But this depends upon transliterating the Greek form of Nero Caesar into Hebrew and then performing the calculation with this spelling, nrôn qsr. And even this spelling is generally considered a defective form of nrôn qysr, with the letter yodh missing (which is permissible, but not well attested in Hebrew texts with the name of Caesar in them. You can see that this is getting problematic: it assumes that readers, at least some readers, have knowledge of Hebrew not only Greek, and would choose both the right name to transliterate and the appropriate way to transliterate. A lot of contingencies.

A host of other name possibilities, generally in Greek, have also been suggested.

Anyway, I am getting a little beyond your question. In short, there was a base-10 system in use, the number would have been represented with Greek letters (and is in the earliest manuscripts), and 666 is a superior textual tradition.

The number of the beast appears in our earliest fragment of Revelation, the Oxyrhynchus Papyri, as 616, not 666 and both numbers were used by the early church.

It is thought the numbers are derived from giving numerical values to letters, as a code, and the two different values come from the different Greek and Latin spellings of the name and title "Nero Caesar".

Acccording to Bruce M. Metzger in "A Textual Commentary on the Greek New Testament":
"Perhaps the change was intentional, seeing that the Greek form Neron Caesar written in Hebrew characters (nrwn qsr) is equivalent to 666, whereas the Latin form Nero Caesar (nrw qsr) is equivalent to 616."

As a follow up, have humans generally used base 10? and is it for the obvious reason that we have 10 fingers?

6 is man's number (as in the 6th day God created Adam). 7 is considered God's number. 777 would be a "trinity" while 666 would be a fallen trinity.