After the actual cost of a public improvement authorized under section 727.23 of the Revised Code has been ascertained, the legislative authority of the municipal corporation shall by ordinance assess, in the manner provided in the resolution of necessity adopted under section 727.12 of the Revised Code, upon the lots and lands enumerated in the estimated assessment adopted under section 727.23 of the Revised Code, that portion of the total cost of the improvement to be paid for by special assessments and such assessments as to each lot or parcel of land, shall be increased or decreased in the same proportion to the estimated assessment on each such lot or parcel of land as the actual cost of the improvement bears to the estimated cost of the improvement upon which the estimated assessment was based. Such assessments shall be payable as provided in the resolution of necessity adopted under section 727.12 of the Revised Code, and shall be final upon the adoption of the ordinance provided for in this section, unless the ordinance and resolution are amended pursuant to section 727.251 of the Revised Code. No publication of the ordinance provided for in this section need be made under the provisions of sections 731.21 and 731.22 of the Revised Code.

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Assessments made under this section shall be filed with the clerk of the legislative authority and shall be open to public inspection.