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Property, Plant, and Equipment - Schedule of Property, Plant, and Equipment (Details)
$ in Millions
3 Months Ended 6 Months Ended
Feb. 28, 2022
USD ($)
building
Feb. 28, 2022
USD ($)
Feb. 28, 2021
USD ($)
Aug. 31, 2021
USD ($)
Property, Plant and Equipment [Line Items]        
Total property, plant, and equipment, at cost $ 864.6 $ 864.6   $ 845.3
Less: Accumulated depreciation and amortization (600.5) (600.5)   (576.2)
Property, plant, and equipment, net $ 264.1 264.1   269.1
Gain on sale of building   2.3 $ 0.0  
Sold        
Property, Plant and Equipment [Line Items]        
Building classified as held for sale | building 1      
Property, plant and equipment held for sale $ 6.6 6.6    
Gain on sale of building 2.3      
Land        
Property, Plant and Equipment [Line Items]        
Total property, plant, and equipment, at cost 22.2 22.2   22.4
Buildings and leasehold improvements        
Property, Plant and Equipment [Line Items]        
Total property, plant, and equipment, at cost 200.5 200.5   198.0
Machinery and equipment        
Property, Plant and Equipment [Line Items]        
Total property, plant, and equipment, at cost $ 641.9 $ 641.9   $ 624.9