When the petition is filed, the board shall fix a time for a public hearing upon the petition and the clerk shall give notice thereof by publication in such newspapers published in the county as designated by the board, not exceeding three, at least once in each week for two weeks, the first publication to be at least two weeks before the date of hearing, and by posting a copy of the notice in the post office in each incorporated city or town in the county, and at some public place in each election precinct of the county.