Revenue Recognition - Summary of Contract Balances (Detail) - USD ($) $ in Millions		6 Months Ended
		Feb. 28, 2022	Aug. 31, 2021
Contract With Customer Asset And Liability [Line Items]
Contract liabilities	[1]	$ 37.5	$ 36.4
Change in contract liabilities	[1]	1.1
Accounts Receivable, Net
Contract With Customer Asset And Liability [Line Items]
Contract assets		10.1	5.9
Change in contract assets		4.2
Inventories
Contract With Customer Asset And Liability [Line Items]
Contract assets		7.1	$ 6.7
Change in contract assets		$ 0.4

[1] Contract liabilities balance includes deferred revenue within the scope of Revenue from Contracts with Customers (Topic 606).