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Comprehensive Income - Tax Amounts Allocated to Components of Other Comprehensive Income (Loss) (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 28, 2022	Feb. 28, 2021	Feb. 28, 2022	Feb. 28, 2021
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	$ 6.4	$ 8.7	$ (3.9)	$ 15.4
Other comprehensive (loss) income, tax	(0.4)	(0.3)	(0.8)	(0.8)
Other comprehensive income (loss) items, net of tax	6.0	8.4	(4.7)	14.6
Foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	4.8	6.7	(7.1)	11.3
Other comprehensive (loss) income, tax	0.0	0.0	0.0	0.0
Other comprehensive income (loss) items, net of tax	4.8	6.7	(7.1)	11.3
Prior service cost
Accumulated Other Comprehensive Income (Loss) [Line Items]
Amortization of defined benefit pension items, before tax	0.7	0.7	1.4	1.4
Amortization of defined benefit pension items, tax	(0.2)	(0.1)	(0.4)	(0.3)
Amortization of defined benefit pension items, after tax	0.5	0.6	1.0	1.1
Actuarial losses
Accumulated Other Comprehensive Income (Loss) [Line Items]
Amortization of defined benefit pension items, before tax	0.9	1.3	1.8	2.7
Amortization of defined benefit pension items, tax	(0.2)	(0.2)	(0.4)	(0.5)
Amortization of defined benefit pension items, after tax	0.7	1.1	1.4	2.2
Total defined benefit pension plans, net
Accumulated Other Comprehensive Income (Loss) [Line Items]
Other comprehensive (loss) income, before tax	1.6	2.0	3.2	4.1
Other comprehensive (loss) income, tax	(0.4)	(0.3)	(0.8)	(0.8)
Other comprehensive income (loss) items, net of tax	$ 1.2	$ 1.7	$ 2.4	$ 3.3

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