Datamængden er ubegrænset.

Because Danish usually puts the definite article at the end of the noun.

• datamængde = data amount / amount of data
• datamængden = the data amount / the amount of data

So -en here means the. This is very common in Danish:

• bil → bilen = the car
• bog → bogen = the book
• datamængde → datamængden = the amount of data

Yes. Danish very often forms compound nouns as a single word.

Here, datamængde is made from:

• data = data
• mængde = amount / quantity

Together, datamængde means amount of data. Then the definite ending -en is added:

• datamængde = amount of data
• datamængden = the amount of data

This is much more natural in Danish than writing it as separate words.

Er is the present tense of at være = to be.

So:

• jeg er = I am
• du er = you are
• det er = it is
• datamængden er = the data amount is

In this sentence, er links the subject datamængden with the description ubegrænset.

It is an adjective meaning unlimited.

It is built from:

• begrænse = to limit
• begrænset = limited
• ubegrænset = unlimited

The prefix u- often works like English un-:

• mulig = possible
• umulig = impossible

So ubegrænset is a very transparent word once you know the parts.

Good question, because this can be confusing.

The short answer is: the -t is part of the adjective form ubegrænset itself, not just a special ending added because of the noun in this sentence.

This word comes from a past participle-type adjective, like begrænset and interesseret. In these adjectives, the -et form is the normal singular form you often see.

So in:

• Datamængden er ubegrænset

the form ubegrænset is simply the correct adjective form meaning unlimited.

A useful comparison:

• en interesseret person = an interested person
• et interesseret barn = an interested child
• personen er interesseret = the person is interested

Notice that interesseret stays the same in these singular cases. Ubegrænset behaves similarly.

Because Danish usually does not use a separate the with a noun unless special circumstances apply.

Instead, the definite article is attached to the noun:

• en mængde = an amount
• mængden = the amount

So datamængden already includes the.

A separate determiner can appear in phrases like:

• den store bil = the big car

But in a simple noun like datamængden, the ending does the job by itself.

Yes, very much so.

The structure is:

• Datamængden = subject
• er = verb
• ubegrænset = subject complement / adjective

So it follows the same basic pattern as:

• The car is red
• The amount of data is unlimited

This makes it a very beginner-friendly Danish sentence.

Yes. That is also correct.

There are two natural ways to express this idea:

• Datamængden er ubegrænset
• Mængden af data er ubegrænset

The first is a compound noun, which is very Danish in style.
The second uses an of-phrase, more like English the amount of data.

Both are grammatical. The compound version often sounds more compact and idiomatic.

It is correct, but in everyday mobile-plan or internet-plan language, Danish often uses slightly different phrasing, such as:

• Du får ubegrænset data = You get unlimited data
• Der er ubegrænset data = There is unlimited data

So Datamængden er ubegrænset is grammatical and clear, but it can sound a bit formal or technical depending on context.

A simple learner-friendly approximation is:

• datamængden ≈ DA-ta-meng-den

A few pronunciation notes:

• æ in mæng is somewhat like the vowel in English cat, but not exactly the same.
• The g in mængde is not strongly pronounced like English g in go.
• The d in many Danish words is often softer than English d.

If you want to sound natural, it is better to listen to native audio, because Danish pronunciation is often less phonetic than the spelling suggests.

A simple approximation is:

• ubegrænset ≈ oo-be-GREN-set

Helpful notes:

• u sounds like oo in food
• græn contains æ, again somewhat like the vowel in cat
• The final -et is not pronounced as strongly as an English et

As with datamængden, listening to native pronunciation is very helpful here, because Danish vowel quality and reduced endings can be hard to guess from spelling alone.