Знак принадлежит зданию.

Because the verb принадлежать means to belong (to), and in Russian it requires the thing or person that something belongs to to be in the dative case.

So:

• знак = the sign, in the nominative (the subject)
• зданию = to the building, in the dative

Russian expresses to the building with the dative ending, not with a separate word like English to.

The dictionary form is здание meaning building.

Here the noun is changed from здание to зданию because it is in the dative singular.

A useful pattern:

• здание = nominative singular
• зданию = dative singular

Many neuter nouns ending in -ие form the dative singular in -ию.

Because Russian often uses case endings instead of separate prepositions where English uses words like to.

In English:

• belongs to the building

In Russian:

• принадлежит зданию

The idea of to the building is already built into the form зданию, so no extra word is needed.

You can tell from both case and verb agreement.

• знак is in the nominative, which is the normal subject case.
• принадлежит is third-person singular, matching знак because знак is singular.
• зданию is in the dative, so it cannot be the subject here.

So the structure is:

• Знак = subject
• принадлежит = verb
• зданию = indirect object-like complement required by the verb

Принадлежит is the third-person singular present tense form of принадлежать.

So:

• я принадлежу = I belong
• ты принадлежишь = you belong
• он / она / оно принадлежит = he / she / it belongs

In this sentence, знак is singular, so the verb is singular too: принадлежит.

Not always. Принадлежать can mean:

• to belong to someone as property
• to be part of an organization or group
• to be assigned to or associated with something

So Знак принадлежит зданию usually means the sign belongs to the building in the sense of ownership or association.

It does not automatically mean the sign is physically attached to the building. If you wanted to say that, Russian would more naturally use a different verb, such as one meaning is attached or is on the building.

Yes. Russian word order is more flexible than English because the case endings show the grammatical roles.

The neutral order here is:

• Знак принадлежит зданию.

You could also say:

• Зданию принадлежит знак.

That is still grammatical, but it sounds more marked and may emphasize the building.

So changing the order usually changes focus or emphasis, not the basic meaning.

Russian has no articles.

So знак can mean:

• a sign
• the sign

and зданию can mean:

• to a building
• to the building

Context tells you which is meant. English must choose an article, but Russian usually does not.

It is pronounced roughly like:

Znak pree-nad-lee-ZHEET ZDAH-nee-yu

Stress:

• Знак
• принадлежи́т
• зда́нию

A few notes:

• принадлежи́т has the stress on the last syllable.
• зда́нию has the stress on the first syllable.
• The ending -ю sounds like yu.