Serijski broj je u radnom nalogu.

• serijski = serial
• broj = number
• je = is
• u = in / inside
• radnom = work-related / of a work order, in the required case form
• nalogu = order / work order, in the required case form

So structurally, it is literally Serial number is in work order.

Because broj is the subject of the sentence, so it stays in the nominative singular:

• serijski broj = the serial number

You would see broja in other grammatical roles, for example:

• nema serijskog broja = there is no serial number

Here, though, broj is simply the thing being talked about, so nominative is used.

Je is the 3rd person singular of the verb biti (to be), so it means is.

The sentence has the structure:

• Serijski broj = subject
• je = is
• u radnom nalogu = in the work order

So it works just like English The serial number is in the work order.

Because u can take different cases depending on meaning:

• u + locative = in / inside / at a place
• u + accusative = into a place, showing movement

Here there is no movement. The serial number is already located there, so Serbian uses the locative:

• u radnom nalogu = in the work order

Compare:

• Serijski broj je u radnom nalogu. = The serial number is in the work order.
• Upisao sam broj u radni nalog. = I entered the number into the work order.

Radnom is the adjective radni in the locative singular masculine/neuter form, because it has to agree with nalogu.

In Serbian, adjectives agree with the noun in:

• gender
• number
• case

Since nalog is masculine singular, and here it is in the locative after u, the adjective also changes:

• nominative: radni nalog
• locative: u radnom nalogu

The base form is nalog. After u meaning in, the noun goes into the locative singular, and nalog becomes nalogu.

So:

• nalog = work order (dictionary form, nominative)
• u nalogu = in the work order

Because the adjective is there too, the full phrase becomes:

• u radnom nalogu

Formally, nalogu can look the same in both dative and locative. But in this sentence it is locative, because it follows the preposition u with the meaning in a place.

So although the ending may match dative, the function here is locative:

• u radnom nalogu = in the work order

Serbian has no articles like English a or the.

So serijski broj can mean:

• a serial number
• the serial number

The exact meaning depends on context. In this sentence, English would usually translate it as the serial number because the context probably makes it specific.

Yes. Serbian word order is more flexible than English because case endings show grammatical relationships.

The neutral order here is:

• Serijski broj je u radnom nalogu.

But you could also hear:

• U radnom nalogu je serijski broj.

That version puts more focus on where the serial number is.

So the basic meaning stays the same, but the emphasis changes.

Sometimes, depending on context, yes.

Serbian u literally means in, but with documents it can often correspond to English in or on, depending on how English naturally phrases it.

• u radnom nalogu = in the work order / on the work order

If you are talking about information contained in a document, English often prefers on the work order, even though Serbian uses u.

Serijski broj is the standard, natural way to say serial number in Serbian.

It is an adjective + noun structure:

• serijski = serial
• broj = number

Broj serije would mean something more like the number of the series or series number, which is not the normal equivalent in most technical contexts.

So if you mean serial number, serijski broj is the usual expression.

A simple pronunciation guide is:

SE-ri-yski broy ye oo RAD-nom na-LO-gu

A few useful notes:

• j is pronounced like English y
• broj sounds roughly like broy
• u is like oo in food
• g is always hard, like in go

In standard Serbian, you normally keep je in a sentence like this.

So:

• Serijski broj je u radnom nalogu. = correct standard form

In headlines, notes, or very informal clipped language, Serbian sometimes omits forms of to be, but for normal full sentences, learners should use je here.