Other (Income) Expense (Details) - USD ($) $ in Millions	3 Months Ended
	Nov. 30, 2024	Nov. 30, 2023
Interest (income) expense, net:
Interest expense	$ 6.1	$ 6.4
Interest income	(10.1)	(5.5)
Interest (income) expense, net	(4.0)	0.9
Miscellaneous expense, net:
Non-service components of net periodic pension cost	1.0	1.1
Foreign currency transaction losses	0.1	0.6
Other items	1.4
Other items		(0.6)
Miscellaneous expense, net	2.5	1.1
Total other (income) expense	$ (1.5)	$ 2.0