(a) In addition to the posting of ordinances and resolutions, Council may, by motion passed by the majority of the members thereof, require the publication of certain resolutions and ordinances in any newspaper printed in Ohio and of general circulation in the City.
(b) Posting shall not affect the publication requirements with respect to bidders for the construction of public improvements and the sale of bonds, notices of which shall be published, in not more than two newspapers printed in Ohio and of general circulation in the City, not less than two nor more than four consecutive weeks.