Intangibles and Other Assets, Net - Identifiable Intangible and Other Assets (Detail) - USD ($) $ in Millions	Feb. 28, 2023	Aug. 31, 2022
Intangibles and Other Assets by Major Class [Line Items]
Finite-Lived Intangible Assets, Net, Total	$ 43.0	$ 47.3
Intangible assets not subject to amortization	2.4	2.4
Prepaid and other assets	76.4	32.4
Operating lease ROU assets	$ 50.0	$ 54.2
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]	Total Intangible and other assets, net	Total Intangible and other assets, net
Nonqualified savings plan investments	$ 45.1	$ 40.3
Debt issuance costs, net	6.8	8.7
Assets held for sale	0.3	3.8
Total Intangible and other assets, net	224.0	189.1
Customer Relationships
Intangibles and Other Assets by Major Class [Line Items]
Finite lived intangible assets gross	87.5	87.5
Accumulated amortization	(67.6)	(66.1)
Other Intangible Assets
Intangibles and Other Assets by Major Class [Line Items]
Finite lived intangible assets gross	42.7	42.4
Accumulated amortization	$ (19.6)	$ (16.5)