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Significant Accounting Policies - Other Long-Term Assets and Liabilities (Details)
$ in Millions
Aug. 31, 2023
USD ($)
employee
Aug. 31, 2022
USD ($)
Other Long-Term Assets [Abstract]    
Deferred costs and other assets $ 29.9 $ 28.1
Investments in debt and equity securities 7.2 11.9
Pensions plans in which plan assets exceed benefit obligation 12.4 8.0
Total other long-term assets $ 49.5 48.0
Number of former employees covered under life insurance policy | employee 56  
Other Long-Term Liabilities [Abstract]    
Deferred compensation and postretirement benefits other than pensions $ 45.6 44.4
Deferred revenues 47.6 53.1
Unrecognized tax position liabilities, including interest 23.4 22.0
Self-insurance liabilities 3.8 3.7
Product warranty and recall costs 8.8 4.9
Other 0.0 0.8
Total other long-term liabilities 129.2 128.9
Customers with Rebate, Marketing, and Trade Promotion Programs    
Other Long-Term Liabilities [Abstract]    
Deferred revenues $ 47.6 $ 53.1