It is proper and desirable, at most of our meetings, for speakers to talk on mathematical topics to which they may themselves have made significant contributions. In general at such meetings we shall all understand the broad outline, but the details are likely to be obscure to most of us. The presidential address, I have always thought, is in rather a different category. The speaker should ensure that his audience, though originally lacking deep knowledge of the chosen topic, should go away with the impression that they not only understand every word but could also reproduce the arguments, say to a class of sixth-form mathematicians. Since our association is mainly concerned with the refreshment of school mathematics and mathematicians, I hope to talk about a part of numerical mathematics which could be taught in school, which uses “standard” mathematics, and which springs from standard mathematics. I start with a rather lengthy introduction on the general principles of error analysis.