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Goodwill and Intangible Assets - Changes in Goodwill (Details) - USD ($) $ in Millions	6 Months Ended
	Feb. 28, 2021	Feb. 29, 2020
Goodwill [Roll Forward]
Goodwill, Beginning Balance	$ 1,080.0	$ 967.3
Provisional additions from acquired businesses	0.0	147.8
Adjustments to provisional amounts from acquired businesses	0.0	(23.9)
Foreign currency translation adjustments	4.2	(1.6)
Goodwill, Ending Balance	$ 1,084.2	$ 1,089.6

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

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- 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.

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- 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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- Definition

Amount of increase (decrease) from adjustments after acquisition date under purchase accounting of an asset representing the future economic benefits arising from other assets acquired in a business combination that are not individually identified and separately recognized.

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

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