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It seems that there is a consensus that the PIE roots for ten and hundred are, respectively, *dekṃ and *kṃtóm. There also seems to be a consensus that *kṃtóm is a shortened version of *dekṃtóm. These two roots are strongly related, both morphologically (sharing the syllable *-km-) 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)kṃtóm was formed by appending the syllable *-to- to the root *dekṃ, 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: *kṃtóm means (a unit of) tens. So, the combination of these two morphemes (*dekṃ + *kṃtóm), meaning "ten units of ten", would have given rise to *(de)kṃtóm.

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

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?

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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. – Noldorin Oct 13 '11 at 0:04
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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? – Alek Storm Nov 3 '11 at 20:08
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@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. – Otavio Macedo♦ Nov 3 '11 at 22:35
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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. – Mark Beadles Dec 3 '12 at 15:20

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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,

  1. *dékm was an e-grade form with a zero-grade form *dkm1.
  2. *-tóm was a suffix. Neither source conjectures as to its nature2.
  3. The initial d of *dkmtóm was lost, presumably for phonotactic reasons as happened with *dʰ(é)ǵʰōm.

So those two sources essentially say "hundred <- ten + suffix". . This is not a complete explanation, but it's certainly suggestive that two of the authors you mention essentially agree. We don't know the nature of the suffix but maybe it's better that we don't, rather than suggest things like "ten-ness" or "units of". This would give "ten" as the older word from which "hundred" is derived, which makes sense culturally too

1In PIE a series of forms like *CéC, *CeC, *CóC, *CoC, *CC were related in a mechanism called ablaut which was used to express grammatical function.

2Although I note that *tom/tóm/tam is reconstructed as an accusative demonstrative or pronoun, e.g. in Schleicher's fable.

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Lenghtened grade is not the same as stress. – Anixx Dec 2 '12 at 20:32
@Anixx Indeed, corrected. – Mark Beadles Dec 3 '12 at 15:13

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