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Property, Plant, and Equipment - Schedule of Property, Plant, and Equipment (Details) $ in Millions	3 Months Ended	12 Months Ended
	Nov. 30, 2021 USD ($) building	Aug. 31, 2021 USD ($) building
Property, Plant and Equipment [Line Items]
Total property, plant, and equipment, at cost	$ 846.2	$ 845.3
Less: Accumulated depreciation and amortization	(585.2)	(576.2)
Property, plant, and equipment, net	$ 261.0	$ 269.1
Held-for-sale
Property, Plant and Equipment [Line Items]
Building classified as held for sale | building	1	1
Property, plant and equipment held for sale	$ 6.6
Land
Property, Plant and Equipment [Line Items]
Total property, plant, and equipment, at cost	22.1	$ 22.4
Buildings and leasehold improvements
Property, Plant and Equipment [Line Items]
Total property, plant, and equipment, at cost	198.0	198.0
Machinery and equipment
Property, Plant and Equipment [Line Items]
Total property, plant, and equipment, at cost	$ 626.1	$ 624.9

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