Let an indirectly measurable variable Y be represented as a function of finite number of directly measurable variables X_1, \linebreak X_2, ..., X_n. We introduce maximum absolute and relative inaccuracies of second order of Y - this idea is a continuation of our research of a new principle for representing the maximum inaccuracies of Y using the inaccuracies of X_1, X_2, ..., X_n. Using inaccuracies of second order we determine the maximum inaccuracies of indirectly measurable variable Y with quadratic approximation which gives their values more precisely. We give algorithmically an easily applicable method for determining their numerical values. The defined by us maximum inaccuracies of second order give the opportunity for more precise determination of the inaccuracy when measuring indirectly measurable variables