Jeg vil slå ordet op i ordbogen, hvis jeg ikke forstår betydningen.

Because slå op is a verb + particle expression in Danish. In this sentence, it means look up.

When there is an object, Danish often places that object between the verb and the particle:

slå ordet op = look the word up

So op belongs with slå, even though they are separated. This is very common in Danish.

Compare:

Jeg vil slå ordet op.
Jeg vil slå det op.

Both are natural. You should think of slå op as one vocabulary item, even if it gets split in the sentence.

Here vil expresses intention or what the speaker plans to do. It can often be translated as English will, but it is not always used in exactly the same way.

In Danish, the present tense is also often used for future meaning, so vil is not the only way to talk about the future. In this sentence, vil gives the sense of:

If that happens, I will / I intend to do this.

So jeg vil slå ordet op sounds like a decision or willingness to do it.

Because they are in the definite form.

In Danish, the definite article is usually added to the end of the noun instead of appearing as a separate word like English the.

Here are the basic forms:

• et ord → ordet
• en ordbog → ordbogen
• en betydning → betydningen

So:

• ordet = the word
• ordbogen = the dictionary
• betydningen = the meaning

This is one of the most important differences between Danish and English nouns.

Because ord is a neuter noun in Danish.

Danish nouns have two grammatical genders:

• common gender: usually takes en in the indefinite form and -en in the definite form
• neuter gender: usually takes et in the indefinite form and -et in the definite form

Since it is et ord, the definite form is ordet.

By contrast:

• en ordbog → ordbogen
• en betydning → betydningen

Because Danish normally uses i with books, dictionaries, and things you look inside.

So:

• i en bog = in a book
• i en ordbog = in a dictionary

This is the standard preposition with slå noget op when you are looking something up in a dictionary or reference work.

Because hvis jeg ikke forstår betydningen is a subordinate clause.

In Danish, word order changes between main clauses and subordinate clauses.

In a main clause, ikke usually comes after the finite verb:

Jeg forstår ikke betydningen.

In a subordinate clause, ikke usually comes before the finite verb:

hvis jeg ikke forstår betydningen

This is a very common pattern and something English speakers often need time to get used to.

Because hvis means if in a conditional sense.

The speaker is talking about something that may or may not happen:

If I do not understand the meaning, I will look the word up.

By contrast, når is used more for when something is expected, regular, or repeated.

Compare:

• Hvis jeg ikke forstår betydningen, vil jeg slå ordet op.
  = If I do not understand the meaning, I will look it up.

• Når jeg ikke forstår et ord, slår jeg det op.
  = When(ever) I do not understand a word, I look it up.

So hvis is the correct choice for this sentence.

Yes, absolutely.

You can say:

Hvis jeg ikke forstår betydningen, vil jeg slå ordet op i ordbogen.

That is very natural Danish.

But when the hvis clause comes first, the word order in the main clause changes. Danish main clauses follow the verb-second rule, so you get:

..., vil jeg ...

not

..., jeg vil ...

That inversion is an important feature of Danish sentence structure.

Because betydning is the normal word for the meaning of a word or expression.

So when you are talking about vocabulary, definitions, or what a word means, betydning is the most natural choice.

mening often means things like:

• opinion
• point
• sense in a broader way

So in this sentence, betydningen is the better and more precise word.

It depends on which Danish comma system is being used.

Many learners will see a comma before subordinate clauses such as one introduced by hvis, so this version is very normal:

Jeg vil slå ordet op i ordbogen, hvis jeg ikke forstår betydningen.

In modern Danish, it is also possible to write the sentence without that comma, depending on the comma style being followed.

So the comma here is not strange at all, and many textbooks and writers still use it regularly.

The sentence has two parts:

Main clause:
Jeg vil slå ordet op i ordbogen

Subordinate clause:
hvis jeg ikke forstår betydningen

A simple breakdown is:

• Jeg = subject
• vil = finite verb / modal verb
• slå ordet op = infinitive phrase
• i ordbogen = prepositional phrase
• hvis jeg ikke forstår betydningen = conditional subordinate clause

This is a good example of two important Danish patterns at the same time:

• verb-second word order in the main clause
• different negation placement in the subordinate clause