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Significant Accounting Policies - Property, Plant and Equipment (Details) - USD ($)
$ in Millions
 12 Months Ended
Aug. 31, 2024
Aug. 31, 2023
Aug. 31, 2022
Property, Plant and Equipment [Line Items]      
Depreciation expense $ 51.4 $ 51.1 $ 53.8
Total property, plant, and equipment, at cost 999.7 961.8  
Less: Accumulated depreciation and amortization (695.8) (664.2)  
Property, plant, and equipment, net 303.9 297.6  
Land      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost 22.3 23.0  
Buildings and leasehold improvements      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost 218.7 210.9  
Machinery, equipment, and information technology      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost $ 758.7 $ 727.9  
Minimum | Buildings and leasehold improvements      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 3 years    
Minimum | Machinery, equipment, and information technology      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 2 years    
Maximum | Buildings and leasehold improvements      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 40 years    
Maximum | Machinery, equipment, and information technology      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 15 years