Investments and Fair Value Measurements - Fair Value Inputs (Details) - Fair Value, Measurements, Recurring - USD ($) $ in Millions	Aug. 26, 2023	Aug. 27, 2022
Assets that fund deferred compensation:
Domestic equity funds	$ 1.7	$ 1.2
International equity funds	0.1	0.1
Fixed income funds		0.1
Total assets at fair value	1.8	1.4
Contingent consideration
Earnout liability	18.4	39.8
Total liabilities at fair value	18.4	39.8
Level 1
Assets that fund deferred compensation:
Domestic equity funds	1.7	1.2
International equity funds	0.1	0.1
Fixed income funds		0.1
Total assets at fair value	1.8	1.4
Contingent consideration
Earnout liability	0.0	0.0
Total liabilities at fair value	0.0	0.0
Level 2
Assets that fund deferred compensation:
Domestic equity funds	0.0	0.0
International equity funds	0.0	0.0
Fixed income funds		0.0
Total assets at fair value	0.0	0.0
Contingent consideration
Earnout liability	0.0	0.0
Total liabilities at fair value	0.0	0.0
Level 3
Assets that fund deferred compensation:
Domestic equity funds	0.0	0.0
International equity funds	0.0	0.0
Fixed income funds		0.0
Total assets at fair value	0.0	0.0
Contingent consideration
Earnout liability	18.4	39.8
Total liabilities at fair value	$ 18.4	$ 39.8