Intangibles and Other Assets, Net - Identifiable Intangibles and Other Assets, Net (Detail) - USD ($) $ in Millions	Feb. 29, 2024	Aug. 31, 2023
Intangibles and Other Assets by Major Class [Line Items]
Finite-Lived Intangible Assets, Net, Total	$ 34.9	$ 39.1
Intangible assets not subject to amortization	2.3	2.3
Prepaid and other assets	50.5	56.4
Operating lease ROU assets	$ 70.7	$ 70.6
Operating Lease, Right-of-Use Asset, Statement of Financial Position [Extensible Enumeration]	Total Intangibles and other assets, net	Total Intangibles and other assets, net
Nonqualified savings plan investments	$ 56.4	$ 47.7
Debt issuance costs, net	6.4	6.3
Assets held for sale	0.3	0.3
Deferred tax assets	34.1	33.1
Total Intangibles and other assets, net	255.6	255.8
Customer Relationships
Intangibles and Other Assets by Major Class [Line Items]
Finite lived intangible assets gross	87.5	87.5
Accumulated amortization	(70.6)	(69.1)
Other Intangible Assets
Intangibles and Other Assets by Major Class [Line Items]
Finite lived intangible assets gross	41.8	43.0
Accumulated amortization	$ (23.8)	$ (22.3)