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Significant Accounting Policies - Goodwill and Other Intangibles (Details)
 12 Months Ended
Aug. 31, 2019
USD ($)
reporting_unit
Aug. 31, 2018
USD ($)
reporting_unit
Aug. 31, 2017
USD ($)
Goodwill [Roll Forward]      
Begining balance $ 970,600,000 $ 900,900,000  
Additions from acquired businesses 2,000,000.0 77,000,000.0  
Adjustments to provisional amounts (200,000)    
Foreign currency translation adjustments (5,100,000) (7,300,000)  
Ending balance $ 967,300,000 970,600,000 $ 900,900,000
Weighted Average Amortization Period in Years 17 years    
Amortized intangible assets, gross carrying amount $ 523,900,000 526,200,000  
Accumulated Amortization (199,200,000) (169,200,000)  
Amortization expense of finite-lived intangible assets 30,800,000 $ 28,500,000 28,000,000.0
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]      
Amortization expense in fiscal 2020 30,800,000    
Amortization expense in fiscal 2021 28,000,000.0    
Amortization expense in fiscal 2022 27,000,000.0    
Amortization expense in fiscal 2023 25,900,000    
Amortization expense in fiscal 2024 $ 25,400,000    
Number of reporting units | reporting_unit 1 1  
Goodwill impairment charge $ 0 $ 0 0
Trade Names      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Unamortized trade names, Gross Carrying Amount 141,300,000 141,700,000  
Intangible asset impairment charge $ 0   $ 0
Patents and patented technology      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 12 years    
Amortized intangible assets, gross carrying amount $ 135,700,000 137,200,000  
Accumulated Amortization $ (72,900,000) (62,200,000)  
Trademarks and trade names      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 19 years    
Amortized intangible assets, gross carrying amount $ 27,200,000 27,200,000  
Accumulated Amortization $ (14,500,000) (13,200,000)  
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 $ (39,700,000) (37,500,000)  
Customer relationships      
Goodwill [Roll Forward]      
Weighted Average Amortization Period in Years 21 years    
Amortized intangible assets, gross carrying amount $ 299,200,000 300,000,000.0  
Accumulated Amortization $ (72,100,000) $ (56,300,000)