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Significant Accounting Policies - Selling, Distribution and Administrative Expenses (Details) - USD ($) $ in Millions	12 Months Ended
	Aug. 31, 2023	Aug. 31, 2022	Aug. 31, 2021
Accounting Policies [Abstract]
Other shipping and handling costs	$ 141.7	$ 151.2	$ 132.0
Share-based payment expense	42.0	37.4	32.5
Income tax benefit for share-based compensation	7.2	9.6	6.5
Net excess tax (benefit) expense related to share-based payment cost	1.5	4.8	0.5
Research and development expense	97.1	95.1	88.3
Advertising costs	$ 21.9	$ 19.3	$ 15.9

X

- Definition

Shipping and handling cost incurred during the reporting period, excluding fees billed to customers and costs associated with inbound freight and freight between manufacturing facilities.

+ References

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- Definition

Amount charged to advertising expense for the period, which are expenses incurred with the objective of increasing revenue for a specified brand, product or product line.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 720
-SubTopic 35
-Name Accounting Standards Codification
-Section 50
-Paragraph 1
-Subparagraph (b)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147483406/720-35-50-1

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Amount of expense for award under share-based payment arrangement. Excludes amount capitalized.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section S99
-Paragraph 1
-Subparagraph (SAB Topic 14.F)
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147479830/718-10-S99-1

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-Topic 718
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Amount of difference between reported income tax expense (benefit) and expected income tax expense (benefit) computed by applying domestic federal statutory income tax rate to pretax income (loss) from continuing operation, attributable to expense for award under share-based payment arrangement. Excludes expense determined to be nondeductible upon grant or after for award under share-based payment arrangement.

+ References

Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef
-Topic 740
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 12
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147482685/740-10-50-12

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-Name Accounting Standards Codification
-Section 35
-Paragraph 2
-SubTopic 740
-Topic 718
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147480887/718-740-35-2

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Amount of tax benefit for recognition of expense of award under share-based payment arrangement.

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Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 718
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
-Paragraph 2
-Subparagraph (h)(1)(i)
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The aggregate costs incurred (1) in a planned search or critical investigation aimed at discovery of new knowledge with the hope that such knowledge will be useful in developing a new product or service, a new process or technique, or in bringing about a significant improvement to an existing product or process; or (2) to translate research findings or other knowledge into a plan or design for a new product or process or for a significant improvement to an existing product or process whether intended for sale or the entity's use, during the reporting period charged to research and development projects, including the costs of developing computer software up to the point in time of achieving technological feasibility, and costs allocated in accounting for a business combination to in-process projects deemed to have no alternative future use.

+ References

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Topic 730
-SubTopic 10
-Name Accounting Standards Codification
-Section 50
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-URI https://asc.fasb.org//1943274/2147482916/730-10-50-1

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-Topic 912
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-Topic 985
-SubTopic 20
-Section 50
-Paragraph 1
-Publisher FASB
-URI https://asc.fasb.org//1943274/2147481283/985-20-50-1

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