error bounds on approximate solutions of equations 81 large integral values may be avoided by preliminary or intermediate treatment of the matrix, the creeping decimal error is ever present and may be met only with otherwise unnecessary decimals or with iterative methods.3 The time consumed by this method and the time by the method of all complete reductions were in the ratio of 1 to 3 when using the same equipment in both cases and with the same number handicap, by the same operators.