The Exif:ApertureValue is stored as an APEX value as mandated by various EXIF standards.
The APEX system is a way to calculate exposure and works using base-2 logarithms. The use of base-2 means a rise of one in the value equates to a doubling, which we know as
1 stop; which makes it pretty handy for photographers if they're good with logarithms (which we don't use much nowadays). Do note, however, that 1 stop in aperture means doubling of the square of the F-number -- for example, going from f/2.8 to f/4 is 1 stop because 42 = 2 * 2.82 (approximately).
To convert from APEX to F-numbers, use the following equation:
ApertureValue (Av) = log2 (F-number)2 = 2 log2 (F-number)
⇒ F-number = 2Av / 2
f/8.0 to it's APEX value
Log2(8) = 3
3 * 2 = 6 (or
6/1 as a fraction)
To convert the
6/1 APEX value back to f/8...
6/2 = 3
2^3 = 8 giving us back f/8.0
Wikipedia: APEX System.
ExifTool: Exif Tags
APEX—The Additive System of Photographic Exposure (PDF) – Contains tables and equations, but no calculation examples.
JEITA CP-3451 Exif 2.2 (PDF) – Contains conversion equations.