(a) Whenever it shall be made to appear to the satisfaction of the county court of any county that any section, or part of section of land in the county is in such small or irregular subdivisions as respects ownerships thereof, that the subdivisions or any of them cannot be accurately or conveniently designated in the assessment list or tax list in the usual or ordinary manner of designating subdivisions of land, it shall be the duty of the county court to order the county surveyor of the county to make and return to the county recorder of the county a plat, with accompanying marginal or footnotes, of the section or part section, whereupon it shall be the duty of the county surveyor to promptly comply with and obey such orders.
(b) In the plats and by the marginal or footnotes which he or she shall make and return, he or she shall show the relative size and position of the several subdivisions and the area of each, which subdivisions shall be designated as "lots" and shall be numbered consecutively in like manner and order, insofar as practicable, as is done in the case of fractional sections in the surveys and plats made under the direction of the United States Bureau of Land Management.