Main evidence: Universal belief (including experts), coherence of theory, directly testable implications that I deal with on a day-to-day basis (fuel cells), lots more directly testable predictions (brownian motion, all the rest of chemistry, thermodynamics, solid and fluid mechanics...)
Let's put it this way, if I encountered the kind of evidence that would be required to cast it into doubt, I'd have to revise my belief in pretty much everything. Cartesian demon level.
Maybe 15 bits? Mostly metauncertainty.
EDIT: I feel profoundly unqualified as a mere human to be tossing around that kind of certainty, but I'm going to leave it.
How much confidence do you place in the scientific theory that ordinary matter is made of discrete units, or 'atoms', as opposed to being infinitely divisible?
More than 50%? 90%? 99%? 99.9%? 99.99%? 99.999%? More? If so, how much more? (If describing your answer in percentages is cumbersome, then feel free to use the logarithmic scale of decibans, where 10 decibans corresponds to 90% confidence, 20 to 99%, 30 to 99.9%, etc.)
This question freely acknowledges that there are aspects of physics which the atomic theory does not directly cover, such as conditions of extremely high energy. This question is primarily concerned with that portion of physics in which the atomic theory makes testable predictions.
This question also freely acknowledges that its current phrasing and presentation may not be the best possible to elicit answers from the LessWrong community, and will be happy to accept suggestions for improvement.
Edit: By 'atomic theory', this question refers to the century-plus-old theory. A reasonably accurate rewording is: "Do you believe 'H2O' is a meaningful description of water?".