Business Combinations (Details) - USD ($) $ in Millions		12 Months Ended
	Aug. 17, 2018	Sep. 28, 2018	Sep. 29, 2017	Sep. 30, 2016
Business Combinations [Abstract]
Business Acquisition, Effective Date of Acquisition	Aug. 17, 2018
Payments for acquisitions, net of cash acquired		$ 404.0	$ 13.7	$ 55.6
Consideration transferred		407.1
Contingent consideration arrangements, low range of outcomes		0.0
Contingent consideration arrangements, high range of outcomes		20.0
Contingent consideration liability recorded for business combinations		3.1
Goodwill recognized through business combinations		306.8	9.7
Merger termination fee		$ 0.0	$ 0.0	$ 88.5