Numer licznika jest na rachunku.

Because Polish is using the genitive case here.

Numer licznika literally means number of the meter. In Polish, when one noun belongs to or is connected with another noun, the second noun often goes into the genitive:

• numer licznika = the meter number / the number of the meter
• kolor domu = the color of the house
• drzwi samochodu = the car’s door / the door of the car

The base form is licznik, but in the genitive singular it becomes licznika.

Here licznik means a meter, usually a utility meter such as:

• an electricity meter
• a gas meter
• a water meter

In other contexts, licznik can also mean counter or odometer, so the exact meaning depends on context. In Numer licznika jest na rachunku, it most naturally means meter.

In this sentence, rachunek most likely means bill or invoice.

Polish rachunek can mean different things depending on context, for example:

• bill
• invoice
• check (in a restaurant)
• account in some contexts

Here, because we are talking about a meter number, na rachunku is best understood as on the bill/invoice.

Because the preposition na here means on, and after na Polish uses different cases depending on meaning.

In this sentence, the meaning is location: the number is on the bill. For location, na takes the locative case:

• rachunek → na rachunku

Compare:

• na stole = on the table
• na ścianie = on the wall
• na rachunku = on the bill

So rachunku is the locative singular form of rachunek.

Here jest means is, and in a normal full sentence it should be there.

• Numer licznika jest na rachunku. = The meter number is on the bill.

If you remove jest:

• Numer licznika na rachunku.

that no longer sounds like a normal complete sentence. It feels more like a note, label, or heading.

So in standard spoken and written Polish, jest is the natural choice here.

Yes. Polish word order is fairly flexible, although the emphasis changes.

For example:

• Numer licznika jest na rachunku.
  Neutral: the meter number is on the bill.

• Na rachunku jest numer licznika.
  Emphasizes where it is: on the bill, there is the meter number.

Both are grammatical. The original version is a straightforward neutral statement.

Because Polish has no articles like English a/an/the.

So:

• numer can mean a number or the number
• licznik can mean a meter or the meter
• rachunek can mean a bill or the bill

The exact meaning comes from context. In this sentence, English naturally uses the meter number and the bill, but Polish does not need separate words for that.

No. Numer licznika specifically means meter number.

If you want to say account number, you would usually say:

• numer konta = account number

If you want bill number or invoice number, you might say:

• numer rachunku

So it is important not to confuse:

• numer licznika = meter number
• numer rachunku = bill/invoice number
• numer konta = account number

You might hear something like that in casual speech, but numer licznika is the standard and most natural form.

Polish normally expresses this kind of relationship with the genitive:

• numer licznika

Using od often sounds more colloquial and less precise. A learner should definitely prefer numer licznika.

It can be either, depending on context.

Because Polish has no articles, rachunku could mean:

• on the bill
• on a bill

In real use, context tells you which one is meant. If someone is explaining where to find the meter number, the sentence can mean something general:

• The meter number is on the bill.

If people are discussing one particular document, it can mean:

• The meter number is on the bill.

English looks the same here, but the important point is that Polish leaves this to context.

Yes, it is natural and correct.

It sounds like a clear, practical statement someone might use in everyday life, especially when explaining where to find information on a utility bill.

A very similar natural alternative would be:

• Numer licznika znajduje się na rachunku.

That is slightly more formal and literally means:

• The meter number is located on the bill.

But Numer licznika jest na rachunku is perfectly normal and easy to understand.