Said board of appraisers shall have full authority and it shall be its duty to segregate and classify the acreage of the lands and subdivisions of the same with respect to their respective relative benefits received and to be received from the organization and operation of the district and the construction and maintenance of the district works in accordance with the comprehensive plan therefor adopted by the directors of the district. Those lands receiving the greatest benefits shall be placed in class No. 1; those lands receiving the next greatest benefits shall be placed in class No. 2, and so on down to the class of the least benefits. Those lands receiving no benefits shall be designated "nonbenefited."