Hacker's Guide to Numerical Analysis
"It is not transparent to me why this definition is sensible."<p>Because if I have a six digit meter and I measure 5.0000 volts I know that it is 5.0000 volts. I don't see why that is confusing at all.<p>"Here, yyy has correct one and three significant digits relative to xxx, but incorrect 2 significant digits, since the truncation at x2x_2x2  and y2y_2y2  do not agree even to the first significant digit. "<p>This doesn't make sense. Y has the correct one?<p>I think you might be confused about the purpose of significant digits. SD are intended to be paired with a tolerance. If there is no tolerence quote with the number, it is meaningless to talk about significant digits. You arbitrarily defined the tolerance as +/0.5 (half a unit). That is not always true, almost never true. Consider test equipment, not every multimeter is going to be +/0.5mV, some might be +/-.3uV. It varies.