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Significant Accounting Policies - Goodwill and Other Intangibles (Details)
 12 Months Ended
Aug. 31, 2022
USD ($)
Aug. 31, 2021
USD ($)
Aug. 31, 2020
USD ($)
intangible_asset
Goodwill [Roll Forward]      
Beginning balance $ 1,094,700,000 $ 1,080,000,000  
Additions from acquired businesses   10,000,000.0  
Adjustments to provisional amounts from acquired businesses 2,300,000    
Foreign currency translation adjustments (12,700,000) 4,700,000  
Ending balance 1,084,300,000 1,094,700,000 $ 1,080,000,000
Gross Carrying Amount 677,500,000 682,800,000  
Accumulated Amortization (322,000,000.0) (284,400,000)  
Amortization expense of finite-lived intangible assets 41,000,000 40,700,000 41,700,000
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]      
Amortization expense in fiscal 2023 42,900,000    
Amortization expense in fiscal 2024 38,500,000    
Amortization expense in fiscal 2025 30,900,000    
Amortization expense in fiscal 2026 28,300,000    
Amortization expense in fiscal 2027 26,400,000    
Goodwill impairment charge 0 0 $ 0
Number of unimpaired intangible assets | intangible_asset     12
Trade Names      
Goodwill [Roll Forward]      
Indefinite-lived trade names 173,700,000 174,800,000  
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]      
Intangible asset impairment charge 0 0 $ 1,400,000
Number of impaired intangible assets | intangible_asset     1
Patents and patented technology      
Goodwill [Roll Forward]      
Gross Carrying Amount 160,800,000 164,600,000  
Accumulated Amortization (116,000,000.0) (104,400,000)  
Trademarks and trade names      
Goodwill [Roll Forward]      
Gross Carrying Amount 27,200,000 27,200,000  
Accumulated Amortization (18,300,000) (17,100,000)  
Distribution network      
Goodwill [Roll Forward]      
Gross Carrying Amount 61,800,000 61,800,000  
Accumulated Amortization (47,300,000) (45,000,000.0)  
Customer relationships      
Goodwill [Roll Forward]      
Gross Carrying Amount 427,700,000 429,200,000  
Accumulated Amortization (140,400,000) (117,900,000)  
ABL      
Goodwill [Roll Forward]      
Beginning balance 1,022,200,000 1,012,600,000  
Additions from acquired businesses   6,900,000  
Adjustments to provisional amounts from acquired businesses 2,300,000    
Foreign currency translation adjustments (10,300,000) 2,700,000  
Ending balance 1,014,200,000 1,022,200,000 $ 1,012,600,000
ISG      
Goodwill [Roll Forward]      
Beginning balance 72,500,000 67,400,000  
Additions from acquired businesses   3,100,000  
Adjustments to provisional amounts from acquired businesses 0    
Foreign currency translation adjustments (2,400,000) 2,000,000.0  
Ending balance $ 70,100,000 $ 72,500,000 $ 67,400,000