# What is the relationship between the PIE roots *dekṃ and *kṃtóm?

It seems that there is a consensus that the PIE roots for ten and hundred are, respectively, *deḱṃ and *ḱṃtóm. There also seems to be a consensus that *ḱṃtóm is a shortened version of *deḱṃtóm. These two roots are strongly related, both morphologically (sharing the syllable *-ḱm-) and semantically (a hundred is ten times ten). But what exactly is the nature of this relationship? Researching the subject, I have found some accounts:

• Menninger, 1992: *(d)ḱṃtóm was formed by appending the syllable *-to- to the root *deḱṃ, which turned the number ten into a noun (something like "ten-ness"). In other words, the Proto-Indo-European speakers conceived a hundred essentially as a ten-ness (of tens).

• Anthony, 2007: *ḱṃtóm means (a unit of) tens. So, the combination of these two morphemes (*deḱṃ + *ḱṃtóm), meaning "ten units of ten", would have given rise to *(de)ḱṃtóm.

• Quiles and López-Menchero, 2011: The tens were normally formed with the units followed by the suffix *-dḱṃta ("group of ten"). For example, thirty is *trídḱṃta (*tri + *-dḱṃta). According to this analysis, the word for hundred was formed by *deḱṃ + *-dḱṃta, which somehow produced the word *(d)ḱṃtóm.

These three explanations are very similar, but they also seem to be slightly different from each other. Are they really different or (what is probably the case) am I missing the big picture here?

• Interesting question. Remember however that the PIE roots themselves are quite uncertain. Shared consonant or vowel patterns by simply be commonalities of the language as a whole. Oct 13, 2011 at 0:04
• Oct 14, 2011 at 4:45
• I'm not sure if this is possible to answer without simply repeating each researcher's explanation. They share certain features, like segmenting *<i>dekṃ</i> and *<i>kṃtóm</i> into multiple segments, but each achieves this differently. What sort of answer would you like? Nov 3, 2011 at 20:08
• @AlekStorm For example, in all three explanations, there is a reference to some word for "a group or unit of tens": *dekṃto, *-dkṃta and *kṃtóm. Are they three different words or just three forms of the same word (inflected for case, perhaps)? Or maybe the three explanations are mutually exclusive and there is no consensus on the matter, yet... I'm looking for an answer that addresses these concerns. Nov 3, 2011 at 22:35
• By the way, the km(t) element in all the above has been conjectured by some to be from a PIE form < *ḱomt- 'hand', but I don't know how solid that is. Dec 3, 2012 at 15:20

One further intriguing side note is given by Quiles (2007):

...PIE kmtóm, hundred, (probably from *dkmtóm, a zero-grade suffixed form of dékm, ten)...

a view closely echoed by Anthony (2007) but without the explicit reference to ablaut:

...Proto-Indo-European *k’ṃtom probably was a shortened version of *dek’ṃtom, a word that included the Proto-Indo-European root *dek’ṃ 'ten'.

That is,