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Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($) $ in Millions	3 Months Ended
	Nov. 30, 2021	Nov. 30, 2020
Goodwill [Roll Forward]
Goodwill, Beginning Balance	$ 1,094.7	$ 1,080.0
Foreign currency translation adjustments	(3.7)	0.6
Goodwill, Ending Balance	1,091.0	1,080.6
ABL
Goodwill [Roll Forward]
Goodwill, Beginning Balance	1,022.2	1,012.6
Foreign currency translation adjustments	(3.0)	0.4
Goodwill, Ending Balance	1,019.2	1,013.0
ISG
Goodwill [Roll Forward]
Goodwill, Beginning Balance	72.5	67.4
Foreign currency translation adjustments	(0.7)	0.2
Goodwill, Ending Balance	$ 71.8	$ 67.6

X

- Definition

Amount after accumulated impairment loss of an asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 210
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-03(10)(1))
-URI http://asc.fasb.org/extlink&oid=120398452&loc=d3e534808-122878

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-Publisher FASB
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X

- Definition

Amount of foreign currency translation gain (loss) which increases (decreases) an asset representing future economic benefits from other assets acquired in a business combination that are not individually identified and separately recognized.

+ References

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