Fabrikationsfejlen er i elapparatet.

Because Danish, like English and especially German, often makes compound nouns by joining words together.

Here:

• fabrikation = manufacture / production
• fejl = fault / error / defect

So fabrikationsfejl means manufacturing defect or production defect.

Then the ending -en is added to make it definite:

• fabrikationsfejl = a manufacturing defect
• fabrikationsfejlen = the manufacturing defect

This is very normal in Danish. Instead of writing several separate words, Danish usually combines them into one noun.

The ending -en is the definite article suffix for many singular nouns in Danish.

In English, you say:

• the defect

In Danish, you often attach the to the end of the noun:

• fejl = defect / error
• fejlen = the defect

So:

• fabrikationsfejl = manufacturing defect
• fabrikationsfejlen = the manufacturing defect

This happens because Danish usually puts the definite article at the end of the noun instead of using a separate word like English the.

Because Danish normally uses a suffixed definite article.

Compare:

• en fejl = a defect

• fejlen = the defect

• et apparat = an appliance/device
• apparatet = the appliance/device

So in this sentence:

• fabrikationsfejlen = the manufacturing defect
• elapparatet = the electrical appliance

A separate definite word such as den or det is usually only used when there is an adjective before the noun, for example:

• det nye apparat = the new appliance

But with just the noun by itself, Danish usually uses the ending:

• apparatet, not det apparat in this meaning

Because Danish nouns belong to different grammatical genders.

The main ones in modern Danish are:

• common gender
• neuter

The noun apparat is neuter, so:

• et apparat = an appliance / a device
• apparatet = the appliance / the device

By contrast, many other nouns take -en in the definite singular:

• en fejl → fejlen

So the different endings show different noun genders:

• -en often goes with common gender nouns
• -et goes with neuter nouns

That is why you get:

• fabrikationsfejlen
• elapparatet

El- is a very common Danish element meaning electric or electrical.

So:

• elapparat = electrical appliance / electric device

You will see el- in many everyday words, for example:

• elbil = electric car
• elcykel = electric bicycle
• elregning = electricity bill
• elselskab = electricity company

It is a productive pattern in Danish, so once you know el-, many compounds become easier to understand.

Because i usually means in or inside.

So:

• Fabrikationsfejlen er i elapparatet. means that the defect is in the appliance, not just on its surface.

This is similar to English:

• in the appliance

If the meaning were more like on the appliance or at the appliance, Danish might use a different preposition depending on the context. But for something located internally, i is the natural choice.

Yes. This is a very basic and normal Danish sentence pattern:

• Fabrikationsfejlen = subject
• er = verb
• i elapparatet = prepositional phrase

So the structure is:

Subject + verb + place/location

That matches standard main-clause Danish word order and is very similar to English:

• The manufacturing defect is in the electrical appliance.

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

So:

• jeg er = I am
• du er = you are
• han/hun er = he/she is
• det er = it is

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

• Fabrikationsfejlen er i elapparatet = The manufacturing defect is in the electrical appliance

Danish uses er here exactly where English uses is.

A rough English-friendly guide could be:

fab-ree-ka-SHOHNS-fyle-en air ee EL-a-pa-ra-det

A few important notes:

• fejl does not sound like it looks to an English speaker; it is closer to file or fyle
• er in connected speech is often pronounced quite lightly, something like air or a reduced vowel sound depending on the speaker
• el is usually pronounced like el, not like the English letter name L

The exact pronunciation varies a bit by accent and speed, but the biggest surprise for learners is usually fejl.

Yes, it is understandable and correctly formed. It literally means a defect from the manufacturing process.

That said, depending on context, Danes may also use other words such as:

• produktionsfejl = production defect
• fabrikationsfejl = manufacturing defect
• sometimes just fejl = defect/fault

So the given sentence is grammatical and clear, even if in some situations another compound might sound more common or more specific.

You would remove the definite endings and use the indefinite articles en and et where needed.

Definite:

• Fabrikationsfejlen er i elapparatet.
• The manufacturing defect is in the electrical appliance.

Indefinite:

• En fabrikationsfejl er i et elapparat.
• A manufacturing defect is in an electrical appliance.

So the pattern is:

• en fabrikationsfejl → fabrikationsfejlen
• et elapparat → elapparatet

This is a very useful contrast to learn in Danish.