# French Numbering System - Eighty to Ninety-Nine

Why does French use the format "4 x 20 + n" (n = 0 to 19) for numbers from eighty to ninety-nine?

• It's not so long ago that English speakers did something similar. Didn't some American guy once say something like "Four score and seven years ago...", meaning "87 years ago..."? Commented May 17, 2012 at 13:23
• "c1720 M. Prior Daphne & Apollo 70 We mortals seldom live above fourscore." (OED) Commented May 17, 2012 at 17:13
• Welsh also has a vigesimal system where 80 is pedwar ugain (four-twenties) and 81 is pedwar ugain ac un (four twenties and one). While it also has a, more commonly used, system similar to English where 80 can be wythdeg (eigth tens) and 81 as wythdeg un (eight tens + one). Commented May 17, 2012 at 19:15
• Vigesimal counting is also used in Georgian and (I believe) Ainu. Commented May 20, 2012 at 0:46
• Commented Sep 18, 2014 at 13:11

The strange construction is a relic from a vigesimal system, i.e. a base 20 number system. This I'm just repeating from the Wikipedia page, but it seems it's thought to be of Basque origin.

The French construction is weird, but the Danish system is up there as well:

50 = halvtredsindstyve ( = half-3rd times 20 = 2½ times 20)
60 = tresindstyve ( = three times twenty)
70 = halvfjerdsindstyve ( = half-4th times 20 = 3½ times 20)
80 = firsindstyve (= four times twenty)
90 = halvfemsindstyve (= half-5th times 20 = 4½ times 20)

Note that these have more common short forms halvtreds, tres, halvfjerds, firs, halvfems. On top of the vigesimal thing, note the strange way to say 2½ (etc), half-3rd. As a bonus, Danish has the ones before the tens, e.g.

93 = treoghalvfemsindstyve (3 and half-5th(4½) times 20).

• of Basque origin? Are you sure? Wikipedia says the Gauls had a vigesimal counting system! Commented Sep 18, 2014 at 13:10
• @sergiol, I'm not sure it's of Basque origin. I'm sure that at the time I wrote this answer, the Wikipedia page listed it as one possibility. en.wikipedia.org/w/… Feel free to update the answer if you feel it's out-of-date. Commented Sep 19, 2014 at 4:09