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Income Taxes - Schedule of Reconciliation of Federal Statutory Rate to Total Provision for Income Taxes (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2022	Aug. 31, 2021	Aug. 31, 2020
Income Tax Disclosure [Abstract]
Federal income tax computed at statutory rate	$ 103.7	$ 83.2	$ 68.2
State income tax, net of federal income tax benefit	13.5	10.7	9.7
Federal permanent differences	(4.3)	0.6	0.9
Foreign permanent differences and rate differential	4.3	2.4	2.4
Research and development tax credits	(7.6)	(7.6)	(7.1)
Unrecognized tax benefits	2.1	0.7	1.8
Other, net	(1.8)	(0.1)	0.5
Total provision for income taxes	$ 109.9	$ 89.9	$ 76.4

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Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

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Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to foreign income tax expense (benefit).

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Amount of the difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying the domestic federal statutory income tax rates to pretax income (loss) from continuing operations attributable to tax exempt income, equity in earnings (loss) of an unconsolidated subsidiary, minority noncontrolling interest income (loss), tax holiday, disposition of a business, disposition of an asset, repatriation of foreign earnings, repatriation of foreign earnings jobs creation act of 2004, increase (decrease) in enacted tax rate, prior year income taxes, increase (decrease) in deferred tax asset valuation allowance, and other adjustments.

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