I was watching a really interesting old video from Richard Feynman who was talking about how precise/accurate the predictions of quantum theory agree with observation. The number of decimal places it agrees he said is astounding. He likened it to measuring the circumference of the Earth to within the uncertainty of the width of a human hair. Could someone give me a few examples (or point me to some sources) of some common predictions of quantum theory and the subsequent accuracy of the observations?

Thanks.