Income Taxes - Changes in Unrecognized Tax Benefits (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 26, 2023	Aug. 27, 2022	Aug. 28, 2021
Reconciliation of Unrecognized Tax Benefits, Excluding Amounts Pertaining to Examined Tax Returns [Roll Forward]
Balance at beginning of year	$ 5.0	$ 5.5	$ 5.8
Gross decreases-tax positions in a prior year	(1.5)	(1.1)	(0.9)
Gross increases-tax positions in a prior year	1.0	0.0	0.0
Gross increases-current year tax positions	1.0	0.6	0.6
Balance at end of year	5.5	5.0	5.5
Accrued interest and penalties	0.6	0.7	1.0
Total unrecognized tax benefits	$ 6.1	$ 5.7	$ 6.5