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Goodwill and Purchased Intangible Assets - Schedule of Purchased Intangible Assets (Details) - USD ($) $ in Millions | 12 Months Ended
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Sep. 30, 2021 | Sep. 30, 2020
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 14 years 4 months 24 days | 14 years 8 months 12 days
Gross | $ 756.3 | $ 731.2
Accumulated Amortization | (706.6) | (697.7)
Net | 49.7 | 33.5
Non-amortizable trade names | 417.1 | 384.7
Intangible assets excluding goodwill, gross | 1,173.4 | 1,115.9
Purchased intangible assets, net | $ 466.8 | $ 418.2
Distribution network |  |
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 39 years 1 month 6 days | 39 years 1 month 6 days
Gross | $ 55.4 | $ 55.4
Accumulated Amortization | (35.1) | (33.8)
Net | $ 20.3 | $ 21.6
Technology-related |  |
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 11 years 10 months 24 days | 11 years 10 months 24 days
Gross | $ 104.7 | $ 104.7
Accumulated Amortization | (103.9) | (103.3)
Net | $ 0.8 | $ 1.4
Customer relationships |  |
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 12 years 7 months 6 days | 12 years 9 months 18 days
Gross | $ 572.6 | $ 554.7
Accumulated Amortization | (550.0) | (545.6)
Net | $ 22.6 | $ 9.1
Other |  |
Acquired Finite Lived Intangible Assets [Line Items] |  |
Weighted- Average Life (in years) | 12 years 1 month 6 days | 16 years 3 months 18 days
Gross | $ 23.6 | $ 16.4
Accumulated Amortization | (17.6) | (15.0)
Net | $ 6.0 | $ 1.4

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