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Comprehensive Income - Changes in Components of Accumulated Other Comprehensive Income (Loss) Items (Details) - USD ($) $ in Millions	3 Months Ended				6 Months Ended
	Feb. 28, 2022	Nov. 30, 2021	Feb. 28, 2021	Nov. 30, 2020	Feb. 28, 2022	Feb. 28, 2021
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	$ 2,072.9	$ 2,044.5	$ 1,937.0	$ 2,127.5	$ 2,044.5	$ 2,127.5
Other comprehensive (loss) income before reclassifications					(7.1)	11.3
Amounts reclassified from accumulated other comprehensive loss					2.4	3.3
Net current period other comprehensive income	6.0	(10.7)	8.4	6.2	(4.7)	14.6
Ending balance	2,104.3	2,072.9	1,932.5	1,937.0	2,104.3	1,932.5
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance	(108.9)	(98.2)	(126.5)	(132.7)	(98.2)	(132.7)
Net current period other comprehensive income	6.0	(10.7)	8.4	6.2
Ending balance	(102.9)	(108.9)	(118.1)	(126.5)	(102.9)	(118.1)
Foreign Currency Items
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance		(40.2)		(53.5)	(40.2)	(53.5)
Other comprehensive (loss) income before reclassifications					(7.1)	11.3
Amounts reclassified from accumulated other comprehensive loss					0.0	0.0
Net current period other comprehensive income					(7.1)	11.3
Ending balance	(47.3)		(42.2)		(47.3)	(42.2)
Defined Benefit Pension Plans
Accumulated Other Comprehensive Income (Loss), Net of Tax [Roll Forward]
Beginning balance		$ (58.0)		$ (79.2)	(58.0)	(79.2)
Other comprehensive (loss) income before reclassifications					0.0	0.0
Amounts reclassified from accumulated other comprehensive loss					2.4	3.3
Net current period other comprehensive income					2.4	3.3
Ending balance	$ (55.6)		$ (75.9)		$ (55.6)	$ (75.9)

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A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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Amount after tax, before reclassification adjustments of other comprehensive income (loss).

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Total of all stockholders' equity (deficit) items, net of receivables from officers, directors, owners, and affiliates of the entity which are attributable to the parent. The amount of the economic entity's stockholders' equity attributable to the parent excludes the amount of stockholders' equity which is allocable to that ownership interest in subsidiary equity which is not attributable to the parent (noncontrolling interest, minority interest). This excludes temporary equity and is sometimes called permanent equity.

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