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Significant Accounting Policies - Other Long-Term Assets and Liabilities (Details)
$ in Millions
Aug. 31, 2022
USD ($)
employee
Aug. 31, 2021
USD ($)
Other Long-Term Assets [Abstract]    
Deferred contract costs $ 13.3 $ 12.9
Investments in debt and equity securities 11.9 5.3
Pensions plans in which plan assets exceed benefit obligation 8.0 13.0
Other 14.8 2.7
Total other long-term assets $ 48.0 33.9
Number of former employees covered under life insurance policy | employee 60  
Other Long-Term Liabilities [Abstract]    
Deferred compensation and postretirement benefits other than pensions $ 44.4 43.1
Deferred revenues 53.1 56.7
Unrecognized tax position liabilities, including interest 22.0 19.7
Self-insurance liabilities 3.7 3.9
Product warranty and recall costs 4.9 3.5
Other 0.8 9.3
Total other long-term liabilities 128.9 136.2
Customers with Rebate, Marketing, and Trade Promotion Programs    
Other Long-Term Liabilities [Abstract]    
Deferred revenues $ 53.1 $ 56.7