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Significant Accounting Policies - Goodwill and Other Intangibles (Details)
 12 Months Ended
Aug. 31, 2021
USD ($)
Aug. 31, 2020
USD ($)
intangible_asset
Aug. 31, 2019
USD ($)
Goodwill [Roll Forward]      
Beginning balance $ 1,080,000,000 $ 967,300,000  
Additions from acquired businesses 10,000,000.0 147,800,000  
Adjustments to provisional amounts from acquired businesses   (41,500,000)  
Foreign currency translation adjustments 4,700,000 6,400,000  
Ending balance $ 1,094,700,000 1,080,000,000 $ 967,300,000
Weighted Average Amortization Period in Years 19 years    
Gross Carrying Amount $ 682,800,000 674,000,000.0  
Accumulated Amortization (284,400,000) (242,400,000)  
Amortization expense of finite-lived intangible assets 40,700,000 41,700,000 30,800,000
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]      
Amortization expense in fiscal 2022 41,200,000    
Amortization expense in fiscal 2023 40,500,000    
Amortization expense in fiscal 2024 40,000,000    
Amortization expense in fiscal 2025 31,900,000    
Amortization expense in fiscal 2026 29,100,000    
Goodwill impairment charge 0 $ 0 0
Number of unimpaired intangible assets | intangible_asset   12  
Trade Names      
Goodwill [Roll Forward]      
Indefinite-lived trade names 174,800,000 $ 174,300,000  
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]      
Intangible asset impairment charge $ 0 $ 1,400,000 0
Number of impaired intangible assets | intangible_asset   1  
Patents and patented technology      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 11 years    
Gross Carrying Amount $ 164,600,000 $ 163,600,000  
Accumulated Amortization $ (104,400,000) (89,500,000)  
Trademarks and trade names      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 24 years    
Gross Carrying Amount $ 27,200,000 27,200,000  
Accumulated Amortization $ (17,100,000) (15,800,000)  
Distribution network      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 28 years    
Gross Carrying Amount $ 61,800,000 61,800,000  
Accumulated Amortization $ (45,000,000.0) (42,800,000)  
Customer relationships      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 20 years    
Gross Carrying Amount $ 429,200,000 421,400,000  
Accumulated Amortization (117,900,000) (94,300,000)  
ABL      
Goodwill [Roll Forward]      
Beginning balance 1,012,600,000 907,200,000  
Additions from acquired businesses 6,900,000 142,100,000  
Adjustments to provisional amounts from acquired businesses   (41,900,000)  
Foreign currency translation adjustments 2,700,000 5,200,000  
Ending balance 1,022,200,000 1,012,600,000 907,200,000
ISG      
Goodwill [Roll Forward]      
Beginning balance 67,400,000 60,100,000  
Additions from acquired businesses 3,100,000 5,700,000  
Adjustments to provisional amounts from acquired businesses   400,000  
Foreign currency translation adjustments 2,000,000.0 1,200,000  
Ending balance $ 72,500,000 $ 67,400,000 $ 60,100,000