OK, I took a 1/2.5 second picture, and
ExifTool shows it as 0.4 seconds.
Irfanview Exif shows 1/2.5 seconds.
Interestingly, Adobe Photoshop CS6 Bridge shows it as 0.4 seconds, but opening it in ACR (Adobe Camera Raw) then shows 1/3 second.
Sending it on to Photoshop reports 0.4 again.
But camera markings are only nominal numbers anyway, just some marking to keep humans happy. When shutter speeds were invented 100 years ago, it must have seemed too odd to mark it 1/64 second because our binary computers were not yet known. So they marked it 1, 1/2, 1/4, 1/8, 1/15, 1/30, 1/60, 1/125, 1/250, and still do. A couple of shifts in the numbering, but today, each one actually works as exactly 1/2 of the previous. And it's good enough for us humans.
But the camera
has to use shutter speeds of 1,2,4,8,16,32 seconds, and also 1/(those same numbers), so that each stop is 2x or 1/2x the next one. This 2x difference is the basis of our system.
And for same reason, shutter third stops have to be in numerical multiples of cube root of 2 (1.2599) from the next third stop. (but fstop is different, third stops are cube root of square root of 2, or 1.12246x steps from previous third). Three third stops is exactly 2.0x exposure, or 1.0 stop.
This makes 1/2.5 nominal
have to be 0.3968503 seconds (target goal, not implying this much hardware accuracy). ISO and aperture are very similar situations. f/11 is actually f/11.31 (used in calculations). But the camera always knows how to do it right, and it just sort of glosses over the markings it shows us.
Try setting your camera shutter to 30 seconds, and then timing it with the second hand on your watch.
It will be 32 seconds, promise. It has to be, to honor 2x and 1,2,4,8,16,32, etc.
Which is why the interval timers have to set 33 second intervals to be able to handle multiple 30 second shots.
I've recently done some work regarding this, for example a calculator to show difference in two exposures is at
Exposure Calculator, to Compare Any Two Camera Exposure values, aperture f-stop, Shutter Speed, ISO and EV
It inputs entry of the nominal numbers, but it calculates with the exact numbers. Otherwise, things get rounded off, and equivalent exposures just don't come out as 0.000 difference.
Of interest (to me) is that the bottom of the same page has a second similar calculator, but which uses instead the regular nominal numbers, and its default shows a case that reports about 1/6 stop off due to nominal rounding. And worse, some other online calculators round that to third stops and show it as 1/3 stop off.
It seems better to just use the actual numbers the camera uses.