How precise a vernier scale do I need?

I'm looking to purchase a vernier caliper soon, and I'm unsure as to how precise a scale I need. For most of what I'd be measuring, within 1/32" or 1mm is plenty, but I also want to measure the wear on my bike's disc brake rotors, and I need to replace those when they measure 1.55mm. Is +/-.05mm enough? Or should I spend more to get +/-.02mm? Yes, I know a micrometer would be more precise, but those don't have the versatility of vernier calipers. And yes, I mean vernier not digital. I already have too many things that need batteries