Pension Plans (Details) - Pension Plan - USD ($) $ in Millions	3 Months Ended	9 Months Ended
May 31, 2023	May 31, 2022	May 31, 2023	May 31, 2022
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) [Abstract]
Service cost	$ 1.1	$ 1.3	$ 3.4	$ 3.7
Interest cost	2.2	1.5	6.7	4.6
Expected return on plan assets	(2.3)	(3.5)	(7.1)	(10.4)
Amortization of prior service cost	0.7	0.7	2.0	2.1
Recognized actuarial loss	0.8	0.8	2.3	2.6
Net periodic pension cost	$ 2.5	$ 0.8	$ 7.3	$ 2.6

Amount of gain (loss) from change in actuarial assumptions which (increases) decreases benefit obligation of defined benefit plan. Assumptions include, but are not limited to, interest, mortality, employee turnover, salary, and temporary deviation from substantive plan.

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Amount of prior service cost (credit) recognized in net periodic benefit cost (credit) of defined benefit plan.

+ References

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- Definition

Amount of expected return (loss) recognized in net periodic benefit (cost) credit, calculated based on expected long-term rate of return and market-related value of plan assets of defined benefit plan.

+ References

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Amount of cost recognized for passage of time related to defined benefit plan.

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Amount of net periodic benefit cost (credit) for defined benefit plan.

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- Definition

Amount of cost for actuarial present value of benefits attributed to service rendered by employee for defined benefit plan.

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