Stepper drive resolution

I'm asking for help on understanding stepper motor + gearbox solution, as I've got totally confused during my research on topic.

Story:
Trying to make a sort of precise turning table (at least 1°/step), I've found out that stepper motors may be a good choice, given enough step resolution.

At this point steppers with a gearbox might step in, but info on Web is somewhat different, thus messing everything up.

So, I would like to get straight answers for straight questions:

Questions:

1. What is the real gearbox ratio for stepper like this - 5V Stepper Motor 28BYJ-48 With Drive Test Module Board ULN2003 5 Line 4 Phase? And others, as this 1/64 (for ex.) ratio notation is quite frequent.
Reasoning: My knowledge from university correlates with Wiki article on gearbox ratio. If I'm not mistaken, ratio is usually denoted this way:

[Input Gear] : [Output Gear]


So, if specs are true, 1 revolution of the motor shaft is 64 revolutions of the gearbox output shaft. Who would ever want such stepper?
But, my search on the Arduino forums, Geared Stepper Motor, revealed that somehow it's just the opposite.

2. Is it possible to get such resolution for a stepper motor? Or even higher?
Reasoning: After all, if gearbox ratio is 64:1, and motor shaft step is, say 5°, you have 360°/5°*64=4608 steps, or 360°/4608=0.078° per step overall device, haven't you?

G'day,

For question 1, your knowledge of the standard convention for notation is correct. However, it's worth noting that the listing for the gearbox ratio isn't 1:64, it's 1/64, which is a slightly different notation. My understanding of this notation is the form: $$$$\frac{\text{Output}}{\text{Input}}$$$$. So, in order to make a full revolution at the output (1), there are 64 turns of the input.

To your second question, yes, it's definitely possible to get these resolutions, in theory. The problem is in the transmission from theory to practice. Interestingly, the people in the arduino forum post you linked are actually discussing this. It appears the motor is most commonly used for air conditioner vent actuation, and has a great deal of slop, as well as not Actually having 4096 steps per revolution. If you are intending on using this motor and gear train combination for an application that requires precise movements of the output shaft to within a degree, this may not be a good solution, especially if you're going to be applying any sort of load to it.