Significant digits: foundations, myths and utilization

Scientific text books, journal articles, and all types of other sources of scientific information frequently give certain recommendations and/or make statements of presumed fact concerning the issue of significant digits in scientific computation. Most of these "well-known" facts concerning significance in computation are false. This article discusses the folklore of significant digits, debunks the common cliches, illustrates the actual behavior of computational significance in a typical scenario, and makes recommendations concerning these matters.