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Significant Accounting Policies - Goodwill and Other Intangibles (Details)
 12 Months Ended
Aug. 31, 2020
USD ($)
intangible_asset
reporting_unit
Aug. 31, 2019
USD ($)
Aug. 31, 2018
USD ($)
Acquired Indefinite-lived Intangible Assets [Line Items]      
Intangible asset impairment charge   $ 0 $ 0
Number of unimpaired intangible assets | intangible_asset 12    
Goodwill [Roll Forward]      
Begining balance $ 967,300,000 970,600,000  
Additions from acquired businesses 147,800,000 2,000,000.0  
Adjustments to provisional amounts from acquired businesses (41,500,000) (200,000)  
Foreign currency translation adjustments 6,400,000 (5,100,000)  
Ending balance $ 1,080,000,000.0 967,300,000 970,600,000
Weighted Average Amortization Period in Years 19 years    
Amortized intangible assets, gross carrying amount $ 674,000,000.0 523,900,000  
Accumulated Amortization (242,400,000) (199,200,000)  
Amortization expense of finite-lived intangible assets 41,700,000 30,800,000 28,500,000
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]      
Amortization expense in fiscal 2021 40,700,000    
Amortization expense in fiscal 2022 40,600,000    
Amortization expense in fiscal 2023 40,300,000    
Amortization expense in fiscal 2024 40,100,000    
Amortization expense in fiscal 2025 $ 33,300,000    
Number of reporting units | reporting_unit 1    
Goodwill impairment charge $ 0 0 $ 0
Trade Names      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Unamortized trade names, Gross Carrying Amount 174,300,000 141,300,000  
Intangible asset impairment charge $ 1,400,000    
Number of impaired intangible assets | intangible_asset 1    
Patents and patented technology      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 11 years    
Amortized intangible assets, gross carrying amount $ 163,600,000 135,700,000  
Accumulated Amortization $ (89,500,000) (72,900,000)  
Trademarks and trade names      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 24 years    
Amortized intangible assets, gross carrying amount $ 27,200,000 27,200,000  
Accumulated Amortization $ (15,800,000) (14,500,000)  
Distribution network      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 28 years    
Amortized intangible assets, gross carrying amount $ 61,800,000 61,800,000  
Accumulated Amortization $ (42,800,000) (39,700,000)  
Customer relationships      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 20 years    
Amortized intangible assets, gross carrying amount $ 421,400,000 299,200,000  
Accumulated Amortization $ (94,300,000) $ (72,100,000)