Income Taxes - Schedule of Change in Unrecognized Income Tax Benefit (Details) - USD ($) $ in Millions	12 Months Ended
Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Unrecognized Tax Benefits [Roll Forward]
Unrecognized tax benefits balance at beginning of year	$ 20.1	$ 19.5	$ 17.7
Additions based on tax positions related to the current year	4.2	4.3	3.5
Additions for tax positions of prior years	0.0	1.4	0.1
Reductions for tax positions of prior years	(0.1)	(1.7)	(0.2)
Reductions due to settlements	0.0	(0.5)	0.0
Reductions due to lapse of statute of limitations	(3.1)	(2.9)	(1.6)
Unrecognized tax benefits balance at end of year	$ 21.1	$ 20.1	$ 19.5

A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

No definition available.

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- Definition

Amount of unrecognized tax benefits.

+ References

Reference 1: http://www.xbrl.org/2003/role/exampleRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 55
-Paragraph 217
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Amount of decrease in unrecognized tax benefits resulting from tax positions taken in prior period tax returns.

+ References

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- Definition

Amount of decrease in unrecognized tax benefits resulting from settlements with taxing authorities.

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- Definition

Amount of increase in unrecognized tax benefits resulting from tax positions that have been or will be taken in current period tax return.

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Amount of increase in unrecognized tax benefits resulting from tax positions taken in prior period tax returns.

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Amount of decrease in unrecognized tax benefits resulting from lapses of applicable statutes of limitations.

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