The governing body of any city of the first or second class or of any village may by ordinance create a limited street improvement district for the sole purpose of grading, curbing and guttering any unpaved street or streets or curbing and guttering any paved or unpaved street or streets in the city or village and each district shall be designated as Street Grading, Curbing and Guttering District No. ..... or as Curbing and Guttering District No. ...., as the case may be. The mayor or chairman of the board of trustees and clerk shall, after the passage, approval and publication of such ordinance, publish notice of the creation of any such district or districts one time each week for three weeks in a daily or weekly newspaper of general circulation in the city or village. After the passage, approval and publication of such ordinance and the publication of such notice, the procedure of the mayor and council or chairman and board of trustees in reference to such improvement shall be in accordance with the applicable provisions of sections 16-620 to 16-655 or 17-508 to 17-520.