To ósmy wydatek.

In this sentence, to is not just a simple this/that. In Polish, to is very often used in sentences that identify or classify something:

• To lekarz. = This/That is a doctor.
• To mój brat. = This/That is my brother.
• To ósmy wydatek. = This/That is the eighth expense.

So here to introduces the statement X is Y. It is a very common Polish pattern.

Because in Polish, the present-tense is is often omitted in this kind of sentence.

So both of these are correct:

• To ósmy wydatek.
• To jest ósmy wydatek.

The version without jest is very natural and common. Polish often leaves out the present tense of to be in simple identifying sentences.

Because ósmy has to agree with wydatek in:

• gender
• number
• case

Wydatek is:

• masculine
• singular
• nominative

So the ordinal must also be masculine singular nominative:

• ósmy wydatek

Compare:

• ósma książka = eighth book (feminine)
• ósme okno = eighth window (neuter)

Yes. Wydatek is a masculine inanimate noun.

That matters because adjectives and ordinal numbers in Polish must match the noun. That is why you get:

• ósmy wydatek

and not a feminine or neuter form.

It is in the nominative singular.

This is the basic dictionary form of the noun:

• wydatek

In a sentence like To ósmy wydatek, Polish uses the nominative for this identifying structure.

That is a very good question, because learners often notice sentences like:

• Jan jest nauczycielem. = Jan is a teacher.

There, the predicate noun is often in the instrumental.

But with the structure to + noun phrase, Polish very commonly uses the nominative:

• To nauczyciel.
• To mój brat.
• To ósmy wydatek.

So in this sentence, nominative is the normal choice.

Ósmy is the ordinal form of osiem:

• osiem = eight
• ósmy = eighth

This change is not fully predictable from English, so it is best to learn it as a pair. Polish ordinal numbers often have their own forms, and they behave like adjectives.

For example:

• pierwszy = first
• drugi = second
• trzeci = third
• ósmy = eighth

A rough guide:

• To ≈ toh
• ósmy ≈ OOS-mih
• wydatek ≈ vuh-DAH-tek or vih-DAH-tek as a rough English approximation

A few useful details:

• ó sounds like u in modern Polish
• w sounds like English v
• y has no exact English equivalent, but it is not the same as English ee

Stress:

• TO ÓS-my wy-DA-tek

More exactly, Polish stress is usually on the second-to-last syllable of a word, so:

• ÓSmy
• wyDAtek

No. Polish does not have articles like English a/an and the.

So wydatek can mean:

• an expense
• the expense

and context tells you which one is meant.

That is completely normal in Polish.

Not if you want the same sentence structure.

• To ósmy wydatek = This/That is the eighth expense.
• ten ósmy wydatek is not the same kind of sentence.

Ten is a demonstrative adjective meaning this, and it normally modifies a noun directly:

• ten wydatek = this expense

So to is the right word for the full identifying sentence.

The most neutral order is:

• To ósmy wydatek.

That is the standard way to say it.

If you remove to and say only:

• ósmy wydatek

that is usually just a noun phrase meaning the eighth expense, not a full sentence by itself.

So if you want a complete statement, To ósmy wydatek is the safest and most natural form.

Yes. Ósmy is an ordinal number, but grammatically it behaves very much like an adjective.

So in:

• ósmy wydatek

you have:

• ósmy = adjective-like word modifying the noun
• wydatek = noun

That is why ósmy changes its ending to match the noun, just like a regular adjective would.