Ok, for some reason I can't figure this out, and I think it's because some others don't fully understand it either and provide wrong answers. Here's what I understand - the native stops are multiples of 1.4 (square root of 2). So f/2.8 is one stop slower than f/1.4, and f/4 would be two stops. The big confusion comes when you're at non-native stops - for example, how do you figure out, easily, how many stops between f/3.5 and f/2?
The way I think of it is actually different. There's two scales, one 1.4x the other one. One is f stops 1, 2, 4, 8, 16, 32 One is f stops 1.4, 2.8, 5.6, 11, 22 So going from 1.4 - 2.8 is TWO stops, not one, so at 2.8 you're getting 1/4 the light you do at 1.4. Here's the handy chart for the half and third stops.
I know there's math in there for the relationship, but I just memorized the full stops (1, 1.4, 2.0, 2.8, 4.0, 5.6, 8.0, etc.). You can see that the numbers (roughly) double between two stops. Also, each stop is roughly 1.4X the last stop. That means one stop from 1.0 is 1.4. 2.8 is actually two stops from 1.4 (f/1.4 times 1.4 times 1.4 -- two stops to 2.8).
It is pretty simple to follow once you get your head around it. It is based on a log scale. Take any f stop and double the number and it is two stops down half it and it is two stops open. 1, 2, 4, 8, 16 or if you take stops the in between 1.4, 2.8, 5.6, 11 etc. When you shuffle them like a deck of cards you get the full range 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16. Now the inbetween numbers work the same way 4.0, 4.5, 5.0, 5.6, 6.3, 7.1, 8.0, 9.0, 10, 11, 13, 14, 16. Be aware the numbers are rounded for simplicity. So if you want to remember the most common scale just remember two numbers and multiply or divide by two. On the other hand if you want to remember the whole scale you have to remember 6 numbers and multiply or divide by two. Simpler still is to just count aperture clicks 3 click equal 1 f/stop (unless you have really old equipment and it may be 2 clicks to an f/stop.
Remember that you have 'full stop' and 'partial stops'. The dif between f/2 and f/3.5 is one full stop (f/2 to f/2.8 and a partial stop f/2.8 to f/3.5). The dif between f/2.8 and f/3.5 is 2/3rds of a stop. G