I have been writing about the spacing of decimal and binary floating-point numbers, and about how their relative spacing determines whether numbers round-trip between those two bases. I’ve stated an inequality that captures the required spacing, and from it I have derived formulas that specify the number of digits required for round-trip conversions. I *have not* proven that this inequality holds, but I will prove “half” of it here. (I’m looking for help to prove the other half.)

Continue reading “The Inequality That Governs Round-Trip Conversions: A Partial Proof”