26 hours per Bajoran day...
And this is a tricky one. An "hour" is a unit of some practical significance, in that a deadline of 2.5 hours markedly differs from a deadline of just 2 hours. If Bajor has a customary unit that divides the day in 26, can our Earth heroes call it an "hour" despite it being, say, 68 Earth minutes long? They might get themselves killed that way!
Yet we do get the impression that the Bajoran day indeed is divided in 26, rather than being something like 26.542 Earth hours long. And in dialogue, three days is 78 hours ("All right... But you have 78 hours to leave the station!" is quite suggestive), which suggests the hour is pretty much 1/26 of a day sharp, or else the decimals would mount up at this stage already and we'd get more like 77 or 79 hours.
We might simply argue that the Bajoran hour is almost exactly as long as the Earth hour, while the day is two hours longer - or that the Bajorans use a 22-division day but the translators change that to 26 Earth hours just because the math so conveniently works out. But what do we do with minutes, then? Even a "nearly" 60-minute Bajoran hour would leave the Bajoran minute slightly different from the Earth minute - and thus a phrase "You go in three minutes from now, phaser drawn" or "the core will blow in 2.5 minutes" would be a recipe for disaster.
when an alien says "10 years ago" or "15 years ago" in translation, I expect a rounded-off number in the original units and the original number system, otherwise it's a poor translation.
Heartily agreed. Although the UT might have real trouble analyzing the speech patterns to decide whether precision is warranted or not - and often this would mean analyzing the tail end of a long phrase to decide how a figure at the beginning should be translated, so the UT becomes a time machine.
The time machine argument naturally also affects the "Vulcan years" case. But perhaps the people of the future are conditioned to listening to "UTspeak", which lacks the structure of English and requires the brain to do a further step to accept it as ordinary language? The brain is flexible like that. (Hey, you can read my somewhat broken English, too!)
Timo Saloniemi