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Based on reason and logic; sensible and objective.
Lass uns versuchen, eine rationale Lösung für das Problem zu finden, statt emotional zu reagieren.
Let's try to find a rational solution to the problem instead of reacting emotionally.
The adjective 'rational' is closely related to the noun 'die Ratio' (reason). Both words emphasize the use of intellect and logic instead of feelings.
Eine rationale Analyse der Daten ist für das Projekt entscheidend.
A rational analysis of the data is crucial for the project.
In general usage, 'rational' often describes thought processes or actions. Typical combinations are 'rational denken' (to think rationally), 'rational handeln' (to act rationally), or 'eine rationale Entscheidung treffen' (to make a rational decision).
Trotz der Hektik versuchte sie, eine rationale Entscheidung zu treffen.
Despite the hectic situation, she tried to make a rational decision.
The meaning as a number that can be represented as a fraction belongs exclusively to mathematical terminology. In all other contexts, 'rational' always means 'vernünftig' (reasonable/sensible).
Im Unterricht lernten wir, dass Pi keine rationale Zahl ist.
In class, we learned that pi is not a rational number.
sensible
'sinnvoll' and 'rational' can both describe that something is done with reason and good grounds. 'sinnvoll' sounds very natural in everyday language and emphasizes the benefit of an action or decision. 'rational' sounds more factual and somewhat more formal; it emphasizes that feelings are less important and that the decision is based on logic and reason. For normal advice or practical plans, 'sinnvoll' often fits well. When you mean the contrast with feelings or spontaneous reactions, 'rational' is more precise.
Nach dem Gespräch entscheidet meine Schwester rational und lässt sich nicht von Angst leiten.
After the conversation, my sister makes a rational decision and does not let fear guide her.
Am Wochenende ist es sinnvoll, den Ausflug wegen des Wetters zu verschieben.
On the weekend, it is sensible to postpone the trip because of the weather.