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Comprehensive Income - Tax Amounts Allocated to Components of Other Comprehensive Income (Loss) (Details) - USD ($) $ in Millions	3 Months Ended
	Nov. 30, 2021	Nov. 30, 2020
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	$ (10.3)	$ 6.7
Other comprehensive (loss) income, tax	(0.4)	(0.5)
Other comprehensive (loss) income items, net of tax	(10.7)	6.2
Foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	(11.9)	4.6
Other comprehensive (loss) income, tax	0.0	0.0
Other comprehensive (loss) income items, net of tax	(11.9)	4.6
Prior service cost
Accumulated Other Comprehensive Income (Loss) [Line Items]
Amortization of defined benefit pension items, before tax	0.7	0.7
Amortization of defined benefit pension items, tax	(0.2)	(0.2)
Amortization of defined benefit pension items, after tax	0.5	0.5
Actuarial losses
Accumulated Other Comprehensive Income (Loss) [Line Items]
Amortization of defined benefit pension items, before tax	0.9	1.4
Amortization of defined benefit pension items, tax	(0.2)	(0.3)
Amortization of defined benefit pension items, after tax	0.7	1.1
Total defined benefit pension plans, net
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	1.6	2.1
Other comprehensive (loss) income, tax	(0.4)	(0.5)
Other comprehensive (loss) income items, net of tax	$ 1.2	$ 1.6

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