Bünger, FlorianFlorianBünger2025-07-292025-07-292025-07-10IEEE Transactions on Computers (in Press): (2025)https://hdl.handle.net/11420/56598Let x<inf>0</inf>, y<inf>1</inf>, ...., y<inf>k</inf> be nonzero floating-point numbers in base β ≥ 2 and precision p ≥ 1. Let z := x<inf>0</inf>/ y<inf>1</inf> /.../ y<inf>k</inf>, whereby the divisions are evaluated from left to right, and let ẑ be the corresponding floating-point evaluation according to the IEEE 754 standard in rounding to nearest. We prove that, in absence of underflow and overflow,(Formula presented) provided that (Formula presented). Here (Formula presented) denotes the relative rounding error unit and ω := 2 if β is even and ω := 1 if β is odd. Thus, the relative rounding error of k consecutive floating-point divisions is bounded by ku. This improves on the classical Wilkinson-type bound γk := ku/(1 - ku).en1557-99562025IEEE Computer Soc.Floating-point quotients | IEEE 754 standard | Wilkinson-type relative error estimatesNatural Sciences and Mathematics::510: MathematicsJournal Article10.1109/TC.2025.3585341Journal Article