wertlos
worthless
Having no financial or material value.
Nach der Währungsreform waren die alten Geldscheine plötzlich wertlos.
After the currency reform, the old banknotes were suddenly worthless.

worthless
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worthless
Having no financial or material value.
Nach der Währungsreform waren die alten Geldscheine plötzlich wertlos.
After the currency reform, the old banknotes were suddenly worthless.

The word is made up of 'der Wert' (value) and the ending '-los' (-less). The ending '-los' means 'without', so 'wertlos' literally describes something 'without value'. This structure is found in many adjectives such as 'arbeitslos' (unemployed) or 'hoffnungslos' (hopeless).
Die alten Münzen sind für die Bank wertlos, aber für Sammler nicht.
The old coins are worthless to the bank, but not to collectors.
To express for whom or what something is worthless, you use the preposition 'für' (for) followed by the accusative. This limits the statement to a specific person or a specific purpose.
Dieses Fachbuch ist für einen Anfänger völlig wertlos.
This specialist textbook is completely worthless for a beginner.
'Wertlos' can refer not only to material things with no monetary value, but also to abstract things with no use. Typical examples are 'wertlose Informationen' (worthless information), 'ein wertloser Versuch' (a worthless attempt), or 'ein wertloser Rat' (worthless advice).
Sein Versprechen erwies sich am Ende als wertlos.
His promise turned out to be worthless in the end.
free
'kostenlos' and 'wertlos' can both have to do with money or value, but they mean something very different. 'kostenlos' means that you do not have to pay for something. It can still be useful or good. 'wertlos' means that something has no value, either financially or in the sense of usefulness and significance. The words are easy to confuse because both end in '-los'. The important point is: 'kostenlos' says something about the price. 'wertlos' says something about the value or usefulness.

Im Supermarkt merkt der Kunde, dass der alte Gutschein wertlos ist.
At the supermarket, the customer realizes that the old voucher is worthless.
Am Abend erfährt die Mitarbeiterin, dass der neue Online-Kurs kostenlos ist.
In the evening, the employee finds out that the new online course is free.