Gear Ratio & Design

I have 47 / 9 teeth , ratio 1:5.2222... extruder gears which came with my Reprap kit. Is it bad to use those infinite ratios in gear design generally?

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No, it is considered good design practice. It is called the "hunting tooth" principle. This ensures that all the teeth on both gears engage with each other regularly. For example, if a 10 tooth pinion meshes with a 40 tooth gear, then each tooth on the pinion will mesh with every 4th tooth on the gear, every time. With a hunting tooth, small variations in manufacture are evened out in the bedding in process and the gears run smoother and quieter.

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Quote
WallyL
For example, if a 10 tooth pinion meshes with a 40 tooth gear, then each tooth on the pinion will mesh with every 4th tooth on the gear, every time.

I think you mean that each pinion tooth will always engage with every 10th tooth on the larger gear.

The smoother and quieter part is actually a by-product of the actual intent....to greatly reduce the potential for a non-perfect part (which all parts are in some manner) generating accelerated wear and damage to both parts by always contacting the same surfaces.