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Significant Accounting Policies - Other Long-Term Assets and Liabilities (Details)
$ in Millions
 12 Months Ended
Aug. 31, 2020
USD ($)
Employee
affiliate
Aug. 31, 2019
USD ($)
Other Long-Term Assets [Abstract]    
Deferred contract costs $ 12.3 $ 15.4
Investments in unconsolidated affiliates 6.0 0.0
Tax credits 8.6 0.0
Other 2.6 2.3
Total other long-term assets $ 29.5 17.7
Number of unconsolidated affiliates | affiliate 2  
Number of former employees covered under life insurance policy | Employee 64  
Other Long-Term Liabilities [Abstract]    
Deferred compensation and postretirement benefits other than pensions $ 42.7 41.6
Service-type warranties 53.6 46.4
Uncertain tax positions liability, including interest 18.9 17.6
Other 2.6 5.2
Total other long-term liabilities $ 120.0 110.7
Percentage contribution rate of eligible employee's compensation 3.00%  
Service-Type Warranties    
Other Long-Term Liabilities [Abstract]    
Service-type warranties $ 55.8 $ 46.3