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Significant Accounting Policies - Property, Plant and Equipment (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2020
Aug. 31, 2019
Aug. 31, 2018
Property, Plant and Equipment [Line Items]      
Depreciation expense $ 59.4 $ 57.5 $ 51.8
Total property, plant, and equipment, at cost 802.8 757.7  
Less: Accumulated depreciation and amortization (532.3) (480.4)  
Property, plant, and equipment, net 270.5 277.3  
Land      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost 22.2 22.6  
Total property, plant, and equipment, at cost      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost 192.2 190.7  
Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Total property, plant, and equipment, at cost $ 588.4 $ 544.4  
Minimum | Total property, plant, and equipment, at cost      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 10 years    
Minimum | Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 3 years    
Maximum | Total property, plant, and equipment, at cost      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 40 years    
Maximum | Machinery and equipment      
Property, Plant and Equipment [Line Items]      
Useful lives of plant and equipment, minimum 15 years