O CNPJ e a atividade econômica estão no cadastro.

Because the subject is a compound subject: o CNPJ e a atividade econômica.

In Portuguese, when two things are joined by e (and), the verb normally goes in the plural:

• O CNPJ está no cadastro. = The CNPJ is in the register.
• A atividade econômica está no cadastro. = The economic activity is in the register.
• O CNPJ e a atividade econômica estão no cadastro. = The CNPJ and the economic activity are in the register.

So estão matches the two items together.

Portuguese often uses a definite article before nouns more often than English does, including many abbreviations and official terms.

Here, CNPJ is treated like a masculine noun, so it takes o:

• o CNPJ

This is very natural in Brazilian Portuguese, especially in administrative or bureaucratic language.

A useful detail: CNPJ stands for Cadastro Nacional da Pessoa Jurídica, but in everyday use people often just say o CNPJ to refer to the company’s tax ID number itself.

Because atividade is a feminine singular noun, so it takes the feminine singular article a:

• a atividade econômica

The adjective econômica is also feminine singular because it agrees with atividade.

So the structure is:

• a = feminine singular article
• atividade = noun
• econômica = adjective agreeing with the noun

Because it agrees with atividade, which is feminine.

In Portuguese, adjectives usually agree in gender and number with the noun they describe:

• atividade econômica = feminine singular
• atividades econômicas = feminine plural
• setor econômico = masculine singular
• setores econômicos = masculine plural

So econômica is feminine singular to match atividade.

No is a contraction of:

• em + o = no

So:

• no cadastro literally means in the register / in the record / in the registration system

This kind of contraction is extremely common in Portuguese:

• em + a = na
• em + os = nos
• em + as = nas

Examples:

• no sistema = in the system
• na empresa = in the company
• nos documentos = in the documents

Cadastro is a very common Brazilian Portuguese word in administrative contexts. It can mean things like:

• registration
• record
• registry
• database entry
• registered information

The exact translation depends on context.

In this sentence, no cadastro most likely means something like:

• in the registration record
• in the system
• on file
• in the company’s registered data

So it does not necessarily mean one physical form; it can refer to an official data record or database entry.

It is pronounced letter by letter in Portuguese.

The letters are named in Brazilian Portuguese roughly like this:

• C = cê
• N = ene
• P = pê
• J = jota

So CNPJ is said as:

• cê-ene-pê-jota

A learner may also notice that people often say o CNPJ da empresa to mean the company’s tax ID number.

You might see article omission in headings, labels, or very condensed bureaucratic writing, but in a normal full sentence, o and a sound more natural:

• O CNPJ e a atividade econômica estão no cadastro.

Portuguese generally likes articles more than English does. Omitting them can sound abrupt, list-like, or less natural unless the context is very specific, such as a form field or title.

Yes. Portuguese word order is somewhat flexible, especially for emphasis.

The original sentence is the most neutral:

• O CNPJ e a atividade econômica estão no cadastro.

But you could also say:

• No cadastro estão o CNPJ e a atividade econômica.

This version gives more emphasis to no cadastro and sounds a bit more formal or stylistic.

In everyday administrative language, the original order is usually the clearest and most natural.

Estão is the most straightforward verb here and simply means that those items are present or are included in the record.

But other verbs are possible depending on nuance:

• estão no cadastro = are in the register / are in the system
• constam no cadastro = are listed in the register
• ficam no cadastro = stay/remain in the register

In official or bureaucratic Portuguese, constar is also very common:

• O CNPJ e a atividade econômica constam no cadastro.

That sounds slightly more formal and specifically suggests they appear/listed there.

It is not really about physical location. It is about information being contained in a registration record or system.

Portuguese often uses estar em/no for this kind of idea:

• Os dados estão no sistema. = The data are in the system.
• Seu nome está no cadastro. = Your name is in the register / on file.

So estão no cadastro means that these pieces of information are registered, recorded, or on file.