abzurunden

abzurunden is the zu‑infinitive form of the German separable verb abrunden, meaning "to round off" or "to round down" in different contexts. Grammatically, zu is inserted between the separable prefix ab and the verb stem (ab + zu + runden = abzurunden), and the form appears in infinitive constructions (for example after modal-like expressions, purpose clauses or nouns such as der Versuch, ... abzurunden).

In mathematics and finance, abzurunden commonly refers to reducing precision by rounding numbers downward or to a specified number of decimal places; it contrasts with aufrunden (to round up). In computing and numerical analysis the concept corresponds to floor or truncation operations depending on the rounding rule used. In everyday language abzurunden is used idiomatically to mean "to finish," "to complete," or "to make more rounded or polished" (e.g., to round off a discussion or to smooth an edge in design).

Examples:

- Um das Projekt abzurunden, fügen wir eine Zusammenfassung hinzu. (To round off the project, we add a summary.)

- Die Beträge sind auf zwei Dezimalstellen abzurunden. (Amounts must be rounded to two decimal places.)

Related terms include abrunden, aufrunden, Rundung, and the mathematical operations floor (Gauß-Klammer) and ceiling. The usage and exact meaning depend on context, ranging from precise numerical procedures to figurative senses of completion or refinement.