Exif:ShutterSpeedValue is stored in rational form as an APEX value.
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). (James SnellJames Snell)
To convert from APEX to secondsTo convert from APEX to seconds, we can use the following equationsequation:
ShutterSpeedValue (Tv) = -log2(t)
⇒ t = 2-Tv
For the particular values from your camera, we get:
2(-8643856/1000000) = 1 / 2(8.643856) = 1/400 sec
See also:
Wikipedia: APEX System.
ExifTool: Exif Tags
APEX—The Additive System of Photographic Exposure (PDF)
JEITA CP-3451 Exif 2.2 (PDF)