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Segment Information - Narrative (Details) $ in Millions	6 Months Ended
	Feb. 28, 2025 USD ($) segment	Aug. 31, 2024 USD ($)
Segment Reporting Information [Line Items]
Number of reportable segments | segment	2
Assets	$ 4,581.7	$ 3,814.6
Operating Segments | Acuity Intelligent Spaces
Segment Reporting Information [Line Items]
Assets	$ 214.7	$ 67.6

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