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Significant Accounting Policies - Goodwill and Other Intangibles (Details) | 12 Months Ended
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Aug. 31, 2021 USD ($) | Aug. 31, 2020 USD ($) intangible_asset | Aug. 31, 2019 USD ($)
Goodwill [Roll Forward] |  |  |
Beginning balance | $ 1,080,000,000 | $ 967,300,000 |
Additions from acquired businesses | 10,000,000.0 | 147,800,000 |
Adjustments to provisional amounts from acquired businesses |  | (41,500,000) |
Foreign currency translation adjustments | 4,700,000 | 6,400,000 |
Ending balance | $ 1,094,700,000 | 1,080,000,000 | $ 967,300,000
Weighted Average Amortization Period in Years | 19 years |  |
Gross Carrying Amount | $ 682,800,000 | 674,000,000.0 |
Accumulated Amortization | (284,400,000) | (242,400,000) |
Amortization expense of finite-lived intangible assets | 40,700,000 | 41,700,000 | 30,800,000
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract] |  |  |
Amortization expense in fiscal 2022 | 41,200,000 |  |
Amortization expense in fiscal 2023 | 40,500,000 |  |
Amortization expense in fiscal 2024 | 40,000,000 |  |
Amortization expense in fiscal 2025 | 31,900,000 |  |
Amortization expense in fiscal 2026 | 29,100,000 |  |
Goodwill impairment charge | 0 | $ 0 | 0
Number of unimpaired intangible assets | intangible_asset |  | 12 |
Trade Names |  |  |
Goodwill [Roll Forward] |  |  |
Indefinite-lived trade names | 174,800,000 | $ 174,300,000 |
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract] |  |  |
Intangible asset impairment charge | $ 0 | $ 1,400,000 | 0
Number of impaired intangible assets | intangible_asset |  | 1 |
Patents and patented technology |  |  |
Goodwill [Roll Forward] |  |  |
Weighted Average Amortization Period in Years | 11 years |  |
Gross Carrying Amount | $ 164,600,000 | $ 163,600,000 |
Accumulated Amortization | $ (104,400,000) | (89,500,000) |
Trademarks and trade names |  |  |
Goodwill [Roll Forward] |  |  |
Weighted Average Amortization Period in Years | 24 years |  |
Gross Carrying Amount | $ 27,200,000 | 27,200,000 |
Accumulated Amortization | $ (17,100,000) | (15,800,000) |
Distribution network |  |  |
Goodwill [Roll Forward] |  |  |
Weighted Average Amortization Period in Years | 28 years |  |
Gross Carrying Amount | $ 61,800,000 | 61,800,000 |
Accumulated Amortization | $ (45,000,000.0) | (42,800,000) |
Customer relationships |  |  |
Goodwill [Roll Forward] |  |  |
Weighted Average Amortization Period in Years | 20 years |  |
Gross Carrying Amount | $ 429,200,000 | 421,400,000 |
Accumulated Amortization | (117,900,000) | (94,300,000) |
ABL |  |  |
Goodwill [Roll Forward] |  |  |
Beginning balance | 1,012,600,000 | 907,200,000 |
Additions from acquired businesses | 6,900,000 | 142,100,000 |
Adjustments to provisional amounts from acquired businesses |  | (41,900,000) |
Foreign currency translation adjustments | 2,700,000 | 5,200,000 |
Ending balance | 1,022,200,000 | 1,012,600,000 | 907,200,000
ISG |  |  |
Goodwill [Roll Forward] |  |  |
Beginning balance | 67,400,000 | 60,100,000 |
Additions from acquired businesses | 3,100,000 | 5,700,000 |
Adjustments to provisional amounts from acquired businesses |  | 400,000 |
Foreign currency translation adjustments | 2,000,000.0 | 1,200,000 |
Ending balance | $ 72,500,000 | $ 67,400,000 | $ 60,100,000

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