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Acquisitions (Details) $ in Millions	3 Months Ended
	Nov. 30, 2021 USD ($) acquisition	Aug. 31, 2021 USD ($)	Nov. 30, 2020 USD ($)	Aug. 31, 2020 USD ($)
Business Acquisition [Line Items]
Number of acquisitions completed | acquisition	0
Goodwill	$ 1,091.0	$ 1,094.7	$ 1,080.6	$ 1,080.0
Fiscal 2021 Acquisitions
Business Acquisition [Line Items]
Goodwill	10.0
Identified intangible assets	$ 6.1
Weighted average useful life of acquired intangible assets	11 years
Goodwill expected to be tax deductible	$ 6.9

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- Definition

Weighted average amortization period of finite-lived intangible assets acquired either individually or as part of a group of assets, in 'PnYnMnDTnHnMnS' format, for example, 'P1Y5M13D' represents the reported fact of one year, five months, and thirteen days.

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Line items represent financial concepts included in a table. These concepts are used to disclose reportable information associated with domain members defined in one or many axes to the table.

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The amount of goodwill arising from a business combination that is expected to be deductible for tax purposes.

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Amount of intangible assets, excluding goodwill, acquired at the acquisition date.

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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.

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The number of businesses acquired by the entity during the period.

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