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Other Expense (Details) - USD ($)
$ in Millions
 3 Months Ended 6 Months Ended
Feb. 29, 2024
Feb. 28, 2023
Feb. 29, 2024
Feb. 28, 2023
Interest (income) expense, net:        
Interest expense $ 6.5 $ 7.6 $ 12.9 $ 15.5
Interest income (6.6) (1.9) (12.1) (3.2)
Interest (income) expense, net (0.1) 5.7 0.8 12.3
Miscellaneous expense (income), net:        
Non-service components of net periodic pension cost 1.0 1.2 2.1 2.5
Foreign currency transaction losses (gains) 0.2 (3.8) 0.8 (6.5)
Loss on sale of a business 0.0 0.0 0.0 11.2
Other items (0.6) (1.1) (1.2) (1.8)
Miscellaneous expense (income), net 0.6 (3.7) 1.7 5.4
Total other expense $ 0.5 $ 2.0 $ 2.5 $ 17.7