The word 'explain' has an 'i'. Why does that 'i' disappear when we write it as 'explanation'.
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The question should be: where did that i come from.
If we look at etymonline we find the following: (emphasis mine)
So it seems that the form explane, probably pronounced much like the current version, lost its final e and to reflect the pronunciation in the spelling, an i was added.
The Latin stem explan- of explanare is to explain in English; the stress is on the vowel a and this leads to an enlargement, a becomes ai /ei/. In explanation the stress is on the next syllable. So we might guess the spelling would be explanaition, but obviously one has kept a spelling that is conforming to the Latin noun explanation(em).