Income Taxes - Schedule of Change in Unrecognized Income Tax Benefit (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2021	Aug. 31, 2020	Aug. 31, 2019
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Unrecognized tax benefits balance at beginning of year	$ 17.2	$ 16.6	$ 4.4
Additions based on tax positions related to the current year	5.2	2.3	2.0
Additions for tax positions of prior years	0.1	0.0	10.9
Reductions for tax positions of prior years	(0.1)	(0.4)	0.0
Reductions due to settlements	(4.6)	(1.2)	0.0
Reductions due to lapse of statute of limitations	(0.1)	(0.1)	(0.7)
Unrecognized tax benefits balance at end of year	$ 17.7	$ 17.2	$ 16.6