Property, Plant, and Equipment (Details) - USD ($) $ in Millions	Aug. 26, 2023	Aug. 27, 2022
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	$ 530.4	$ 455.3
Less: Accumulated depreciation	203.1	179.1
Property, plant, and equipment, net	327.3	276.2
Land
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	14.6	14.6
Buildings and building improvements
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	247.3	171.0
Machinery and equipment
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	159.3	142.6
Software
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	52.7	43.8
Transportation
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	7.2	6.5
Construction in progress
Property, Plant and Equipment [Line Items]
Property, plant, and equipment, gross	$ 49.3	$ 76.8