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Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($) $ in Millions	3 Months Ended
	Nov. 30, 2019	Nov. 30, 2018
Goodwill [Roll Forward]
Goodwill, Beginning Balance	$ 967.3	$ 970.6
Additions from acquired businesses	147.8	0.0
Foreign currency translation adjustments	0.4	(3.7)
Goodwill, Ending Balance	$ 1,115.5	$ 966.9

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://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 5
-URI http://asc.fasb.org/extlink&oid=77989000&loc=SL49117168-202975

Reference 2: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 45
-Paragraph 1
-URI http://asc.fasb.org/extlink&oid=99380562&loc=d3e13770-109266

+ Details

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Data Type:	xbrli:monetaryItemType
Balance Type:	debit
Period Type:	instant

X

- Definition

Amount of increase in asset representing future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized resulting from a business combination.

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (b)
-URI http://asc.fasb.org/extlink&oid=108376223&loc=d3e13816-109267

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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

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 350
-SubTopic 20
-Section 50
-Paragraph 1
-Subparagraph (f)
-URI http://asc.fasb.org/extlink&oid=108376223&loc=d3e13816-109267

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X

- Definition

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

+ References

No definition available.

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