Unu miliardo estas granda nombro.

Yes. Miliardo means 1,000,000,000.

This is especially worth noting for English speakers because number words can vary historically between languages. Esperanto uses:

• miliono = 1,000,000
• miliardo = 1,000,000,000
• biliono = 1,000,000,000,000

So in this sentence, unu miliardo means one billion.

Good question. Unu here does not mean an indefinite article like English a/an. It is the actual number one.

So:

• unu miliardo = one billion
• granda nombro = a large number

Esperanto has no indefinite article, but it does have the numeral unu. In this sentence, unu is necessary because it tells you the exact quantity: one billion.

Because Esperanto does not have an indefinite article.

English says:

• a large number

Esperanto simply says:

• granda nombro

Esperanto only has a definite article, la, meaning the. So:

• granda nombro = a large number or just large number, depending on context
• la granda nombro = the large number

Because granda nombro is not a direct object here. It is a predicate expression after estas.

In Esperanto, after esti (to be), you normally use the nominative, not the accusative.

So:

• Unu miliardo estas granda nombro. = correct
• Unu miliardo estas grandan nombron. = incorrect

Also, adjectives agree with the nouns they describe. Since nombro is singular and nominative, the adjective is also singular and nominative:

• granda nombro

Because Esperanto verbs do not change for person or number.

Estas is the present-tense form of esti (to be) and can mean:

• am
• is
• are

depending on the subject.

For example:

• Mi estas = I am
• Li estas = he is
• Ili estas = they are

So in this sentence, estas simply means is because the subject is unu miliardo.

The endings are one of the most important parts of Esperanto grammar.

In this sentence:

• miliard-o: -o shows a noun
• grand-a: -a shows an adjective
• nombr-o: -o shows a noun
• est-as: -as shows present tense

So the sentence is built very regularly:

• unu = one
• miliardo = billion
• estas = is
• granda = large
• nombro = number

This kind of regularity is one reason Esperanto is often easier to analyze than English.

Because nombro means a number as a mathematical quantity, while numero usually means a number used as a label or identifier.

So:

• nombro = number, quantity, mathematical value
• numero = number on a house, bus, shirt, page, ticket, etc.

A billion is a mathematical quantity, so nombro is the correct word.

No. Esperanto adjectives can come before or after the noun.

So both are grammatical:

• granda nombro
• nombro granda

But the normal, most common order is adjective + noun, especially in simple sentences like this one. So granda nombro sounds the most natural.

You usually keep unu when you mean the exact number one billion.

• unu miliardo = one billion

If you say just miliardo, it can sound more general, like a billion as a concept, rather than explicitly naming the quantity one billion. In many contexts people would still understand you, but unu miliardo is the clearest and most standard way to say one billion.

A simple English-friendly approximation is:

OO-noo mee-lee-AR-do ESS-tahs GRAHN-dah NOM-broh

A few useful pronunciation notes:

• u is always like oo in food
• a is like a in father
• e is like e in bet, but often a bit clearer and tenser
• o is like o in for, but pure and short
• the stress is on the second-to-last syllable of each word:
  • U-nu
  • mi-li-AR-do
  • ES-tas
  • GRAN-da
  • NOM-bro

So the stressed parts are U, AR, ES, GRAN, NOM.