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Significant Accounting Policies - Other Long-Term Assets and Liabilities (Details)
$ in Millions
 12 Months Ended
Aug. 31, 2021
USD ($)
employee
Aug. 31, 2020
USD ($)
Other Long-Term Assets [Abstract]    
Deferred contract costs $ 12.9 $ 12.3
Investments in debt and equity securities 5.3 6.0
Pensions plans in which plan assets exceed benefit obligation 13.0 0.0
Tax credits 0.0 8.6
Other 2.7 2.6
Total other long-term assets $ 33.9 29.5
Number of former employees covered under life insurance policy | employee 62  
Other Long-Term Liabilities [Abstract]    
Deferred compensation and postretirement benefits other than pensions $ 43.1 42.7
Deferred revenues 56.7 53.6
Unrecognized tax position liabilities, including interest 19.7 18.9
Self-insurance liabilities 3.9 6.5
Product warranty and recall costs 3.5 2.3
Other 9.3 2.5
Total other long-term liabilities $ 136.2 126.5
Percentage contribution rate of eligible employee's compensation 3.00%  
Customers with Rebate, Marketing, and Trade Promotion Programs    
Other Long-Term Liabilities [Abstract]    
Deferred revenues $ 56.7 $ 53.6