> "Here, y has correct one and three significant digits relative to x, but incorrect 2 significant digits, since the truncation at x_2 and y_2 do not agree even

> "Here, y has correct one and three significant digits relative to x, but incorrect 2 significant digits, since the truncation at x_2 and y_2 do not agree even to the first significant digit. " > This doesn't make sense. Y has the correct one? I think that's a language issue, like "that x̂ agress to x upto p" in the next section. I think what they're trying to say is the following. If you round x = 0.9949 to 1, 2, or 3 significant digits, you get 1, 0.99, or 0.995 respectively. If you round y = 0.9951 to 1, 2, or 3 significant digits, you get 1, 1.0, or 0.995 respectively. So x and y look equal if you round to 1 or 3 significant digits, but not if you round to 2 significant digits.