The datasheet specifies 4V output @ nominal primary current.
So if you put in + or - 15A DC, you'll get + or -4V DC at the output. For AC, you'd need higher peak values, at least 1.414 times the nominal current. These sensors provide 3 times the nominal current as a peak value, so they can copy with 15Arms at a crest factor of three (which is 45A peak). It'll put out up to 3 times the nominal output (say -12V to +12V peak) with such input.
So 45A is the measuring range, intended for peak AC. You shouldn't run more DC or ACrms than the nominal current through it, as it might overheat or overload then.
For your correct uC measurement, you'd want a +/-12V full scale input to cover the full range. If you intend to measure DC only, or pure sine wave AC, you can design your input range smaller, e.g. +/- 8V peak for a 15Arms AC, or +/-5V for +/-15A DC input (always with some reserve)
Scaling (e.g. 4V -> 15A) is always the same.
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