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Other (Income) Expense (Details) - USD ($)
$ in Millions
 3 Months Ended 9 Months Ended
May 31, 2024
May 31, 2023
May 31, 2024
May 31, 2023
Interest (income) expense, net:        
Interest expense $ 6.3 $ 6.3 $ 19.2 $ 21.8
Interest income (8.1) (2.4) (20.2) (5.6)
Interest (income) expense, net (1.8) 3.9 (1.0) 16.2
Miscellaneous (income) expense, net:        
Non-service components of net periodic pension cost 1.2 1.4 3.3 3.9
Foreign currency transaction (gains) losses (1.4) 0.0 (0.6) (6.5)
Loss on sale of a business 0.0 0.0 0.0 11.2
Other items (0.3) (0.7) (1.5) (2.5)
Miscellaneous (income) expense, net (0.5) 0.7 1.2 6.1
Total other (income) expense $ (2.3) $ 4.6 $ 0.2 $ 22.3