Income Taxes - Schedule of Provision for Income Taxes (Details) - USD ($) $ in Millions	12 Months Ended
Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Income Tax Disclosure [Abstract]
Provision for current federal taxes	$ 67.6	$ 65.4	$ 54.6
Provision for current state taxes	16.3	12.8	12.5
Provision for current foreign taxes	25.4	14.4	16.0
Provision for (benefit from) deferred taxes	0.6	(2.7)	(6.7)
Total provision for income taxes	$ 109.9	$ 89.9	$ 76.4

Amount of current federal tax expense (benefit) attributable to income (loss) from continuing operations. Includes, but is not limited to, current national tax expense (benefit) for non-US (United States of America) jurisdiction.

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Amount of current foreign income tax expense (benefit) pertaining to income (loss) from continuing operations.

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Amount of current state and local tax expense (benefit) attributable to income (loss) from continuing operations. Includes, but is not limited to, current regional, territorial, and provincial tax expense (benefit) for non-US (United States of America) jurisdiction.

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