Changes in Stockholders' Equity (Details) - USD ($) $ / shares in Units, shares in Millions, $ in Millions	3 Months Ended
Nov. 30, 2019	Nov. 30, 2018	Sep. 01, 2018
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 1,918.9	$ 1,716.8
Net income	57.0	79.6
Other comprehensive income (loss)	3.8	(6.2)
Share-based payment amortization, issuances, and cancellations	12.6	3.8
Employee stock purchase plan issuances	0.2	0.1
Cash dividends of $0.13 per share paid on common stock	(5.2)	(5.2)
Repurchases of common stock		(25.0)
Ending balance	$ 1,987.3	$ 1,750.9
Cash dividends paid (usd per share)	$ 0.13	$ 0.13
Common Stock Outstanding
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 0.5	$ 0.5
Beginning balance (shares)	39.5	40.0
Share-based payment amortization, issuances, and cancellations (shares)	0.0	0.1
Repurchases of common stock (shares)		(0.2)
Ending balance	$ 0.5	$ 0.5
Ending balance (shares)	39.5	39.9
Paid-in Capital
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	$ 930.0	$ 906.3
Share-based payment amortization, issuances, and cancellations	12.6	3.8
Employee stock purchase plan issuances	0.2	0.1
Ending balance	942.8	910.2
Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	2,295.8	1,999.2
Net income	57.0	79.6
Cash dividends of $0.13 per share paid on common stock	(5.2)	(5.2)
Ending balance	2,347.6	2,060.6
Accumulated Other Comprehensive Loss
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(151.4)	(114.8)
Other comprehensive income (loss)	3.8	(6.2)
Ending balance	(147.6)	(121.0)
Treasury Stock, at cost
Increase (Decrease) in Stockholders' Equity [Roll Forward]
Beginning balance	(1,156.0)	(1,074.4)
Repurchases of common stock		(25.0)
Ending balance	$ (1,156.0)	$ (1,099.4)
ASC 606
Increase (Decrease) in Stockholders' Equity [Roll Forward]
ASC 606 adjustments			$ (13.0)
ASC 606 \| Retained Earnings
Increase (Decrease) in Stockholders' Equity [Roll Forward]
ASC 606 adjustments			$ (13.0)

Aggregate dividends paid during the period for each share of common stock outstanding.

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Amount after tax of increase (decrease) to equity or (increase) decrease to net assets, resulting from the cumulative effect adjustment of a new accounting principle applied in the period of adoption.

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Amount of paid and unpaid cash, stock, and paid-in-kind (PIK) dividends declared, for example, but not limited to, common and preferred stock.

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A roll forward is a reconciliation of a concept from the beginning of a period to the end of a period.

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The portion of profit or loss for the period, net of income taxes, which is attributable to the parent.

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Amount after tax and reclassification adjustments of other comprehensive income (loss).

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Number of shares of stock issued as of the balance sheet date, including shares that had been issued and were previously outstanding but which are now held in the treasury.

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Number of shares issued during the period related to Restricted Stock Awards, net of any shares forfeited.

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Aggregate change in value for stock issued during the period as a result of employee stock purchase plan.

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Value of stock related to Restricted Stock Awards issued during the period, net of the stock value of such awards forfeited.

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Equity impact of the value of stock that has been repurchased during the period and has not been retired and is not held in treasury. Some state laws may mandate the circumstances under which an entity may acquire its own stock and prescribe the accounting treatment therefore. This element is used when state law does not recognize treasury stock.

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Total of all stockholders' equity (deficit) items, net of receivables from officers, directors, owners, and affiliates of the entity which are attributable to the parent. The amount of the economic entity's stockholders' equity attributable to the parent excludes the amount of stockholders' equity which is allocable to that ownership interest in subsidiary equity which is not attributable to the parent (noncontrolling interest, minority interest). This excludes temporary equity and is sometimes called permanent equity.

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