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Significant Accounting Policies - Miscellaneous Income, Net (Details) - USD ($)
$ in Millions
12 Months Ended
Aug. 31, 2022
Aug. 31, 2021
Aug. 31, 2020
Miscellaneous Expense (Income), Net      
Financial Statement Line Items with Differences in Reported Amount and Reporting Currency Denominated Amounts [Line Items]      
Net gain (expense) relating to foreign currency items $ 5.3 $ (1.3) $ (5.9)