Si el resultado es demasiado largo, la profesora nos deja escribir una cifra aproximada.

Because ser is normally used to describe what something is like in a more general or defining way, while estar is more for states or conditions.

Here, demasiado largo describes the result as being too long in form or length, so ser sounds natural:

• El resultado es demasiado largo.

Using está here would sound unusual in standard Spanish.

This is a very common Spanish pattern for a general rule, habit, or repeated situation.

• Si el resultado es demasiado largo, la profesora nos deja escribir una cifra aproximada.

It means something like: whenever that happens, this is what the teacher allows.

Spanish often uses:

• si + present indicative, then
• present indicative

for general conditions.

Also, after si, Spanish does not use the future tense in this kind of sentence. So even if English might say If the result is too long, the teacher will let us..., Spanish still says:

• Si el resultado es demasiado largo, la profesora nos dejará...
  not Si el resultado será...

And there is no subjunctive here, because this is a normal real condition.

Because Spanish usually uses the definite article with a specific person when that person is the subject of the sentence.

So:

• La profesora nos deja... = The teacher lets us...

That sounds natural because we are talking about a particular teacher.

Compare:

• Es profesora. = She is a teacher.
  Here there is no article because it is after ser and gives someone’s profession.
• La profesora está aquí. = The teacher is here.
  Here the article is needed.

Nos means us.

In this sentence, it shows who receives the action of dejar:

• la profesora nos deja escribir
  = the teacher lets us write

So nos is the object pronoun meaning to us / us in this structure.

Spanish object pronouns usually go before a conjugated verb:

• nos deja

But with an infinitive, they can sometimes also attach to the infinitive:

• La profesora nos deja escribir
• La profesora deja escribirnos

However, in this sentence, nos deja escribir is the natural and standard choice.

Dejar + infinitive is a very common way to say let someone do something or allow someone to do something.

Pattern:

• dejar + [person/object pronoun] + infinitive
• or more commonly in practice: [pronoun] + dejar + infinitive

Here:

• la profesora nos deja escribir
• literally: the teacher lets us write

Other examples:

• Mi madre me deja salir. = My mother lets me go out.
• No nos dejan usar el móvil. = They do not let us use the phone.

So deja escribir means allows writing / lets us write.

Because demasiado means too, while muy means very.

That is an important difference:

• muy largo = very long
• demasiado largo = too long

In this sentence, the idea is that the result is longer than is practical or acceptable, so demasiado is the right word.

Because largo agrees with resultado, and resultado is masculine singular.

So:

• el resultado → masculine singular
• largo → masculine singular

If the noun were feminine, the adjective would change:

• la cifra es demasiado larga

Spanish adjectives usually agree in gender and number with the noun they describe.

Not necessarily. In this context, it usually means the answer or result has too many digits, too many decimal places, or is inconveniently long to write out exactly.

So it is often a mathematical or practical idea rather than a physical one.

For example, a result like a long decimal could be described this way. A teacher might then allow an approximate value instead.

A more explicit version could be:

• Si el resultado tiene demasiadas cifras...

But si el resultado es demasiado largo is perfectly understandable.

Here una cifra aproximada means an approximate figure, value, or number.

A small vocabulary point:

• número = number
• cifra can mean digit, figure, or numerical amount depending on context

In everyday mathematical or academic Spanish, cifra aproximada is a natural way to express an approximate figure/value.

So it does not have to mean just one single digit. In context, it means an approximate numerical result.

Because in Spanish, most adjectives normally come after the noun.

So:

• una cifra aproximada

is the standard order.

Also, aproximada agrees with cifra:

• cifra = feminine singular
• aproximada = feminine singular

If the noun were masculine, it would change:

• un número aproximado

Yes. As written, it sounds like a general rule or usual practice:

• If the result is too long, the teacher lets us write an approximate figure.

If you want to talk about one future occasion, Spanish often changes only the main verb:

• Si el resultado es demasiado largo, la profesora nos dejará escribir una cifra aproximada.

Notice that after si, Spanish still keeps the present:

• Si el resultado es...
  not Si el resultado será...

So:

• general rule/habit: Si ..., la profesora nos deja...
• future result: Si ..., la profesora nos dejará...