
grob
rude
Impolite, inconsiderate, or insulting in behavior or expression.
Sei nicht so grob zu deiner kleinen Schwester!
Don't be so rude to your little sister!
rude / rough / approximate
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rude
Impolite, inconsiderate, or insulting in behavior or expression.
Sei nicht so grob zu deiner kleinen Schwester!
Don't be so rude to your little sister!

rough / approximate
Not detailed, exact, or precise; capturing only the basic outlines. Synonymous with 'ungefähr' (approximately) or 'annähernd' (roughly).
Ich habe nur eine grobe Vorstellung davon, wie das Gerät funktioniert.
I have only a rough idea of how the device works.

coarse / rough
Having a rough, not fine or smooth texture or structure.
Der Tisch ist aus grobem, unbehandeltem Holz gefertigt.
The table is made of coarse, untreated wood.

serious / gross
Serious or significant, especially with regard to mistakes, violations, or negligence.
Das Ignorieren der Sicherheitsvorschriften war ein grober Fehler.
Ignoring the safety regulations was a serious mistake.
The meaning of 'grob' depends strongly on the noun it describes. If it refers to a person, it means 'unhöflich' (rude). With an idea or estimate, it means 'ungefähr' (approximate). If it describes a material, it means 'rau' (rough), and with a mistake, it means 'schwerwiegend' (serious).
Sein grober Tonfall hat alle überrascht.
His rude tone surprised everyone.
In the meaning of 'ungefähr' (approximate), 'grob' is often used for plans and estimates. Typical combinations are 'eine grobe Schätzung' (a rough estimate), 'ein grober Plan' (a rough plan), or 'ein grober Überblick' (a rough overview).
Der Architekt zeichnete einen groben Entwurf des Hauses.
The architect drew a rough draft of the house.
When it comes to mistakes or negative behavior, 'grob' intensifies the negative meaning. Common expressions are 'ein grober Fehler' (a serious mistake), 'grobe Fahrlässigkeit' (gross negligence), or 'grober Unfug' (serious nonsense/mischief).
Der Fahrer beging einen groben Verstoß gegen die Verkehrsregeln.
The driver committed a serious violation of traffic rules.
When 'grob' describes rude behavior, it is often used with the preposition 'zu' and the dative to name the person affected.
Er war am Telefon sehr grob zu mir.
He was very rude to me on the phone.
'Grob' can also be used as an adverb to modify a verb. It then means 'not finely' or 'not in detail'.
Schneiden Sie das Gemüse für die Suppe nur grob.
Cut the vegetables for the soup only roughly.
approximately
Both words can express an inexact quantity. „Ungefähr“ generally says that a number is only approximate, whereas „grob“ also indicates a simplified estimate or rough calculation. Use „ungefähr“ for ordinary approximations and „grob“ when the estimate is particularly imprecise or simplified.

Grob geschätzt kostet der Umbau etwa zehntausend Euro.
A rough estimate puts the renovation at around ten thousand euros.
Die Fahrt dauert ungefähr drei Stunden.
The journey takes approximately three hours.