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Significant Accounting Policies - Goodwill and Other Intangibles (Details) | 12 Months Ended
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Aug. 31, 2020 USD ($) intangible_asset reporting_unit | Aug. 31, 2019 USD ($) | Aug. 31, 2018 USD ($)
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Intangible asset impairment charge |  | $ 0 | $ 0
Number of unimpaired intangible assets | intangible_asset | 12 |  |
Goodwill [Roll Forward] |  |  |
Begining balance | $ 967,300,000 | 970,600,000 |
Additions from acquired businesses | 147,800,000 | 2,000,000.0 |
Adjustments to provisional amounts from acquired businesses | (41,500,000) | (200,000) |
Foreign currency translation adjustments | 6,400,000 | (5,100,000) |
Ending balance | $ 1,080,000,000.0 | 967,300,000 | 970,600,000
Weighted Average Amortization Period in Years | 19 years |  |
Amortized intangible assets, gross carrying amount | $ 674,000,000.0 | 523,900,000 |
Accumulated Amortization | (242,400,000) | (199,200,000) |
Amortization expense of finite-lived intangible assets | 41,700,000 | 30,800,000 | 28,500,000
Finite-Lived Intangible Assets, Net, Amortization Expense, Fiscal Year Maturity [Abstract] |  |  |
Amortization expense in fiscal 2021 | 40,700,000 |  |
Amortization expense in fiscal 2022 | 40,600,000 |  |
Amortization expense in fiscal 2023 | 40,300,000 |  |
Amortization expense in fiscal 2024 | 40,100,000 |  |
Amortization expense in fiscal 2025 | $ 33,300,000 |  |
Number of reporting units | reporting_unit | 1 |  |
Goodwill impairment charge | $ 0 | 0 | $ 0
Trade Names |  |  |
Acquired Indefinite-lived Intangible Assets [Line Items] |  |  |
Unamortized trade names, Gross Carrying Amount | 174,300,000 | 141,300,000 |
Intangible asset impairment charge | $ 1,400,000 |  |
Number of impaired intangible assets | intangible_asset | 1 |  |
Patents and patented technology |  |  |
Goodwill [Roll Forward] |  |  |
Weighted Average Amortization Period in Years | 11 years |  |
Amortized intangible assets, gross carrying amount | $ 163,600,000 | 135,700,000 |
Accumulated Amortization | $ (89,500,000) | (72,900,000) |
Trademarks and trade names |  |  |
Goodwill [Roll Forward] |  |  |
Weighted Average Amortization Period in Years | 24 years |  |
Amortized intangible assets, gross carrying amount | $ 27,200,000 | 27,200,000 |
Accumulated Amortization | $ (15,800,000) | (14,500,000) |
Distribution network |  |  |
Goodwill [Roll Forward] |  |  |
Weighted Average Amortization Period in Years | 28 years |  |
Amortized intangible assets, gross carrying amount | $ 61,800,000 | 61,800,000 |
Accumulated Amortization | $ (42,800,000) | (39,700,000) |
Customer relationships |  |  |
Goodwill [Roll Forward] |  |  |
Weighted Average Amortization Period in Years | 20 years |  |
Amortized intangible assets, gross carrying amount | $ 421,400,000 | 299,200,000 |
Accumulated Amortization | $ (94,300,000) | $ (72,100,000) |

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