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Goodwill and Intangible Assets - Narrative (Details) - USD ($) $ in Millions	3 Months Ended		6 Months Ended
	Feb. 28, 2023	Feb. 28, 2022	Feb. 28, 2023	Feb. 28, 2022
Goodwill and Intangible Assets Disclosure [Abstract]
Amortization of intangible assets	$ 9.3	$ 10.3	$ 22.9	$ 20.6
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract]
Amortization expense in fiscal 2023	41.5		41.5
Amortization expense in fiscal 2024	36.9		36.9
Amortization expense in fiscal 2025	29.4		29.4
Amortization expense in fiscal 2026	26.7		26.7
Amortization expense in fiscal 2027	$ 25.2		$ 25.2

X

- Definition

The aggregate expense charged against earnings to allocate the cost of intangible assets (nonphysical assets not used in production) in a systematic and rational manner to the periods expected to benefit from such assets. As a noncash expense, this element is added back to net income when calculating cash provided by or used in operations using the indirect method.

+ References

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-Publisher FASB
-Name Accounting Standards Codification
-Topic 230
-SubTopic 10
-Section 45
-Paragraph 28
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- Definition

Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in next fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

+ References

Reference 1: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
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-SubTopic 30
-Section 50
-Paragraph 2
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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in remainder of current fiscal year.

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in fourth fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in third fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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Amount of amortization for assets, excluding financial assets and goodwill, lacking physical substance with finite life expected to be recognized in second fiscal year following current fiscal year. Excludes interim and annual periods when interim periods are reported from current statement of financial position date (rolling approach).

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