Røgalarmen er i huset.

Because røgalarmen is the definite form: the smoke alarm.

In Danish, definiteness is often added as an ending instead of using a separate word like the in English.

• en røgalarm = a smoke alarm
• røgalarmen = the smoke alarm

So the -en at the end is doing the job that the does in English.

The ending -en marks the noun as definite for a common-gender noun.

For Danish nouns:

• en words usually take -en in the definite singular
• et words usually take -et in the definite singular

So:

• en røgalarm → røgalarmen
• et hus → huset

In this sentence, both nouns are definite:

• røgalarmen = the smoke alarm
• huset = the house

Danish usually does not use a separate word for the in simple noun phrases. Instead, it adds the definite ending directly to the noun.

So:

• et hus = a house
• huset = the house

This is one of the biggest differences from English. English uses a separate article; Danish usually uses a suffix.

Because Danish nouns have grammatical gender, and each noun belongs to a gender class.

• hus is a neuter noun, so it takes et: et hus
• røgalarm is a common-gender noun, so it takes en: en røgalarm

Unfortunately, noun gender often just has to be learned with the noun. That is why it is useful to memorize nouns together with their article:

• en røgalarm
• et hus

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

So:

• jeg er = I am
• du er = you are
• den er = it is

In this sentence, er links the subject and its location:

• Røgalarmen er i huset = the smoke alarm is in the house

Danish uses er in much the same way English uses is.

I means in or inside.

So i huset means in the house or inside the house.

This is the natural preposition if the smoke alarm is located inside the building. Danish often matches English here:

• i bilen = in the car
• i køkkenet = in the kitchen
• i huset = in the house

Yes. Inde i huset is also possible and can sound a bit more explicitly like inside the house.

The difference is roughly:

• i huset = in the house
• inde i huset = inside the house

In many everyday situations, i huset is enough and sounds completely natural.

This sentence has standard Danish main-clause word order:

Subject + verb + adverbial/place

• Røgalarmen = subject
• er = verb
• i huset = place expression

So it follows the same basic pattern as English:

• The smoke alarm is in the house

Danish word order can change if you move another element to the front, but then the verb still stays in second position. For example:

• I huset er røgalarmen.

That is grammatical, but less neutral and more marked. The original sentence is the normal basic version.

Yes. Danish very often makes compound nouns by joining words together.

Here:

• røg = smoke
• alarm = alarm
• røgalarm = smoke alarm

Then the definite ending is added:

• røgalarm → røgalarmen

This is very common in Danish, just as in German and some other languages.

A rough guide is:

• røg sounds something like rugh with a rounded vowel that English does not really have
• alarmen is roughly a-LAHR-men, though the exact Danish sounds are different
• huset is roughly HOO-set

The tricky part for English speakers is ø in røg. It is a front rounded vowel, which English does not normally use. A useful tip is:

1. Make an eh/ay-type vowel shape in the front of your mouth.
2. Round your lips as if saying oo.

That will get you closer to Danish ø.

Because the definiteness is already built into the nouns themselves.

English says:

• the smoke alarm
• the house

Danish says:

• røgalarmen
• huset

So adding a separate word for the would usually be wrong here. In simple definite noun phrases, Danish normally uses the noun ending rather than a separate article.

Yes. Er is present tense, so the sentence means that this is true now.

Compare:

• Røgalarmen er i huset. = present
• Røgalarmen var i huset. = past

So if you want to talk about the smoke alarm’s current location, er is the correct form.