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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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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Cash outflow representing an adjustment to the purchase price of a previous acquisition.

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Acquisitions (Details) $ in Millions	9 Months Ended
Acquisitions (Details) $ in Millions	May 31, 2022 USD ($) acquisition	Aug. 31, 2021 USD ($)	May 31, 2021 USD ($)	Aug. 31, 2020 USD ($)
Business Acquisition [Line Items]
Number of acquisitions completed \| acquisition	0
Cash outflows related to fiscal 2021 acquisitions for working capital settlements	$ (12.2)
Goodwill	1,090.9	$ 1,094.7	$ 1,096.2	$ 1,080.0
Fiscal 2021 Acquisitions
Business Acquisition [Line Items]
Goodwill	10.6
Identified intangible assets	$ 6.7
Weighted average useful life of acquired intangible assets	11 years
Goodwill expected to be tax deductible	$ 7.5