Supplemental Disaggregated Information (Details) $ in Millions	12 Months Ended
Aug. 31, 2019 USD ($) Segment	Aug. 31, 2018 USD ($)	Aug. 31, 2017 USD ($)
Geographic Distribution
Number of reportable segments \| Segment	1
Net sales	$ 3,672.7	$ 3,680.1	$ 3,505.1
Operating profit:	462.9	460.8	527.5
Income before provision for income taxes:	424.9	425.9	492.6
Long-lived assets	297.3	308.4	304.3
Domestic
Geographic Distribution
Net sales	3,277.4	3,292.6	3,123.1
Operating profit:	419.3	419.0	503.3
Income before provision for income taxes:	386.4	386.4	478.5
Long-lived assets	248.9	256.4	252.8
International
Geographic Distribution
Net sales	395.3	387.5	382.0
Operating profit:	43.6	41.8	24.2
Income before provision for income taxes:	38.5	39.5	14.1
Long-lived assets	$ 48.4	$ 52.0	$ 51.5
Sales of lighting solutions, excluding services \| Revenue source
Geographic Distribution
Sales as percentage of total sales (percent)	5.00%	5.00%	5.00%
Lighting and Building Management Solutions \| Sales of lighting solutions, excluding services \| Revenue source
Geographic Distribution
Sales as percentage of total sales (percent)	99.00%	99.00%	99.00%

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