Dette er den fjerde boken.

Because dette is being used as a stand-alone demonstrative pronoun: this / this thing.

In Norwegian:

• dette = this when it stands on its own
• denne = this when it directly goes with a common-gender noun

So:

• Dette er den fjerde boken. = This is the fourth book.
• Denne boken er den fjerde. = This book is the fourth.

A useful shortcut:

• dette = this by itself
• denne + noun = this + noun

Because Norwegian normally uses den/det/de before a definite noun phrase when there is an adjective or ordinal in front of the noun.

Here, fjerde (fourth) comes before boken, so Norwegian needs:

• den fjerde boken

Compare:

• boken = the book
• den fjerde boken = the fourth book

So the extra den is required because the noun is definite and it has a modifier before it.

Yes, in a way it does — and that is normal in Norwegian. This is called double definiteness.

In many definite noun phrases, Norwegian marks definiteness in two places:

1. with den/det/de before the adjective
2. with the definite ending on the noun

So:

• den fjerde boken
  • den = definite marker
  • boken = book with the definite ending -en

English only uses one the, but Norwegian often uses both parts together.

A simple comparison:

• en bok = a book
• boken = the book
• den røde boken = the red book
• den fjerde boken = the fourth book

Because bok is a common-gender noun in Bokmål.

Norwegian articles agree with the gender of the noun:

• en / den for common gender
• et / det for neuter

Since bok takes en in the indefinite form:

• en bok

the definite phrase with an adjective/ordinal uses:

• den fjerde boken

If the noun were neuter, you would use det instead:

• det fjerde kapittelet = the fourth chapter

Boken is the definite singular form of bok.

The forms are:

• en bok = a book
• boken = the book

So in this sentence, boken means the book, not just book.

Yes. For many feminine nouns in Bokmål, you may see either a common-gender pattern or a feminine pattern.

With bok, both of these are possible in Bokmål:

• en bok – boken
• ei bok – boka

So you may also hear or read:

• Dette er den fjerde boka.

That means the same thing.

A learner should know:

• boken is very standard and widely accepted
• boka is also very common, especially in speech and more natural-style writing

Because fjerde is simply the normal form of the ordinal fourth.

Many Norwegian ordinals, especially from første, andre, tredje, fjerde onward, are commonly used in a form ending in -e and do not change much across contexts.

So you get:

• den fjerde boken = the fourth book
• et fjerde kapittel = a fourth chapter

Unlike many ordinary adjectives, fjerde already has the form you need here.

The word order is very normal for a main clause:

• Dette = subject
• er = verb
• den fjerde boken = subject complement / predicate

So the sentence follows the usual pattern:

• Subject + verb + complement

It also fits the Norwegian V2 rule, where the finite verb usually comes in the second position in main clauses. Here:

1. Dette
2. er

So the order is exactly what you would expect.

Yes, but it means something slightly different in feel.

• Dette er den fjerde boken. = This is the fourth book.
• Denne er den fjerde boken. = This one is the fourth book.

Denne usually points more directly to a specific item among others, almost like this one in English.

So if you are identifying something in general, dette is the most natural choice. If you are contrasting one book with others, denne can work.

Yes, often you can.

In Norwegian, ordinal numerals are commonly written with a period:

• 4. = fourth

So this is also possible:

• Dette er den 4. boken.

In running prose, many writers prefer fjerde, while 4. is common in lists, notes, headings, or more practical writing. Both are understandable.