I am only a couple of months late. If any one still cares, fractional f-stops are normally represented in 1/2 stop units, 1/3 stop units, or 1/10 stop units. Digital cameras and light meters normally have a preference menu for which you want to see. Knowing tenths may be good for light ratios, but we can only set our camera lens to thirds.

To compute fractional f-stops (the question):

Due to the area of the circular aperture being Pi R Squared, it turns out that each aperture number is Square root of 2 (1.414) times the previous one (for each next one to have double area). f/2.8 x 1.4 = f/4, f/4 x 1.4 = f/5.6, etc (approximately).

Same said another way, you can think of these as "numbered stops", numbered 0, 1, 2 ,3, etc. This is NOT the aperture numbers, but is just simply sequential numbering of hypothetical stops. Call the first one stop number 0 which matches aperture f/1

Then the aperture is 1.414 to the power of stop number.

Aperture for stop number 0 is 1.414 ^ 0 which is f/1
Aperture for stop number 1 is 1.414 ^ 1 which is f/1.4
Aperture for stop number 2 is 1.414 ^ 2 which is f/2.0
Aperture for stop number 3 is 1.414 ^ 3 which is f/2.8

The point is that intermediate points can have also arbitrary numbered values like this:

[code]
stop number aperture

Stop 3 - 1.414 ^ 3 = f/2.82
Stop 3.1 - 1.414 ^ 3.1 = f/2.93
Stop 3.33 - 1.414 ^ 3.33 = f/3.17
Stop 3.5 - 1.414 ^ 3.5 = f/3.36
Stop 3.67 - 1.414 ^ 3.67 = f/3.56
Stop 3.9 - 1.414 ^ 3.67 = f/3.86
Stop 4 - 1.414 ^ 4 = f/4
[/code]

Note again, this is sequential stop "number" (not aperture, and not seen anyplace else) starting at stop number 0 at f/1, used to compute aperture, as (square root of 2) to the power of stop number.

Thanks for the quick tutorial. Authorhouse