Tatediem: Fractions

Previously we saw the somewhat octal system of Tatediem, but now that we look into the fractional system, we find there are two distinct systems - a quarters-based exponential system, and an ordinals-based analytical system.

We will first look at the fourths-based system. It is basically a 1/4-base system, that has four numbers:

-xùŋge  1/4
-kìdge   2/4
-pàŋge  3/4

-taúm-, -taúŋ-, give sixteenths:

taúŋùŋge    1/16
taúŋìdge     2/16
taúmpàŋge 3/16

pártu- gives 64ths. dértu- gives 128ths and karú gives 256ths. The last two only occur in administrative contexts, and are not known to have been part of colloquial speech ever.

These can combine, in which case only the first part gets the gender congruence marker:

(ga)kìdge taúnùŋge = 2/4 + 1/16 = 5/16
(ye)pàŋge taùmpànge pàrtukìdge karúpàŋge = 3/4 + 3/16 + 2/64 + 3/256 = 192/256 + 48/256 + 8/256 + 3/256 = 251/256 (or somesuch)

The gender congruence always uses nominal prefixes for these for most dialects. A handful of far-south dialects have a twelve-based system instead, with sub-bases 1/3 and 1/4. The letìrti dialect has base 1/4 for the first 'decimal', followed exclusively by base three. In all of these, the fraction can follow on an integer number.

The analytical system takes a ratio, either of the form N raxi (P/Q) or R/Q. N, if present, is treated just like an ordinary numeral (and thus takes the nominal gender prefix). P (or R), however, is marked with the adjectival marker of the gender, and Q is marked with the grammatical gender's nominal dual or plural marker, thus:

wankint raxi wansélx suxuns raxpelì suxuns - two and twelve fifteenths

Raxi is the conjunction 'and', inflected for the plural of the grammatical gender. (It's stem is -əl/-əj, which is reduced in the presence of rax- to raxi.)