Lesson 9: Advanced Numbers
Master large numbers, ordinals, fractions, decimals, multipliers (-obl-), distributives (-op-), and the preposition po.
Overview
At A1/A2 you learned the basic number system up to the hundreds and thousands, as well as ordinal numbers and simple arithmetic. At B1 it is time to extend this foundation to the full range of numerical expression that appears in authentic Esperanto texts: large numbers used in statistics, news, and academic contexts; fractions and decimals for scientific and commercial language; and the highly productive Esperanto number suffixes (-obl-, -on-, -op-) and the distributive preposition po. These forms are used constantly in real Esperanto communication but are rarely taught thoroughly at lower levels.
Esperanto's approach to numbers is both logical and elegant. The suffix system turns any number into a multiplier, fraction, or group marker with complete regularity — no irregular forms, no exceptions. Once you understand the pattern, you can produce and understand any numerical expression immediately, whether it is "one-third" or "in groups of five" or "threefold."
Learning Objectives
- Read and produce large numbers (millions, billions) in Esperanto correctly
- Use ordinal numbers as adjectives that agree with nouns in number and case
- Form and use fractions (duono, triono) and decimals with komo
- Apply the suffixes -obl- (multiplier), -on- (fraction), and -op- (group) and the preposition po productively
Vocabulary
| Esperanto | English | Notes |
|---|---|---|
| miliono | million | 1,000,000 |
| miliardo | billion (thousand million) | 1,000,000,000 |
| biliono | trillion (million million) | BE: billion; use carefully |
| dek mil | ten thousand | 10,000 |
| cent mil | hundred thousand | 100,000 |
| unua | first | ordinal |
| dua | second | |
| tria | third | |
| kvara | fourth | |
| kvina | fifth | |
| sesa | sixth | |
| sepa | seventh | |
| oka | eighth | |
| naŭa | ninth | |
| deka | tenth | |
| dudeka | twentieth | |
| centa | hundredth | |
| mila | thousandth | |
| duono | half (fraction) | 1/2 |
| triono | third (fraction) | 1/3 |
| kvarono | quarter | 1/4 |
| kvino | fifth (fraction) | 1/5 |
| komo | (decimal) comma | in Esperanto, decimals use comma |
| duobla | double, twofold | -obl- |
| triobla | triple, threefold | |
| duope | in pairs, two by two | -op- |
| triope | in threes | |
| po | at the rate of, per, apiece | distributive prep. |
| procento | percent | |
| sumo | sum, total |
Grammar Focus
1. Large Numbers
Esperanto uses a simple additive system for large numbers. Each element is stated from largest to smallest:
| Number | Esperanto |
|---|---|
| 1,000 | mil |
| 10,000 | dek mil |
| 100,000 | cent mil |
| 1,000,000 | unu miliono |
| 5,000,000 | kvin milionoj |
| 1,000,000,000 | unu miliardo |
| 7,800,000,000 | sep miliardoj ok cent milionoj |
miliono and miliardo are nouns, so they take -o/-j/-n as appropriate and are followed by de when a noun follows:
kvin milionoj de homoj — five million people tri miliardoj de dolaroj — three billion dollars
Compare mil (which is a number-word, not a noun):
du mil homoj — two thousand people (no de) cent mil studantoj — a hundred thousand students (no de)
Full example:
La urbo havas du milionojn kaj tricent mil loĝantojn. — The city has 2,300,000 inhabitants.
2. Ordinal Numbers as Adjectives
Ordinal numbers in Esperanto are formed by adding -a to the cardinal number root. They function as full adjectives — they must agree with the noun they modify in number (-j) and case (-n):
| Cardinal | Ordinal | Example |
|---|---|---|
| unu | unua | la unua ĉapitro (the first chapter) |
| du | dua | en la dua ĉambro (in the second room) |
| tri | tria | la trian fojon (for the third time) |
| dek | deka | la deka de julio (the tenth of July) |
| dudek | dudeka | la dudeka jarcento (the twentieth century) |
| cent | centa | la centa datreveno (the hundredth anniversary) |
Compound ordinals:
la dudek-unua jarcento — the twenty-first century la tricent-kvardeka paĝo — the three-hundred-and-fortieth page
Ordinals can become adverbs:
Unue, mi volas diri... — Firstly, I want to say... Due, la dua punkto estas... — Secondly...
3. Fractions with -on-
The suffix -on- appended to a number root creates a fraction noun:
| Number | Fraction | Meaning |
|---|---|---|
| du | duono | half (1/2) |
| tri | triono | third (1/3) |
| kvar | kvarono | quarter (1/4) |
| kvin | kvinono | fifth (1/5) |
| dek | dekono | tenth (1/10) |
| cent | centono | hundredth (1/100) |
duono de la knaboj — half of the boys triono de la tutaj kostoj — one third of the total costs du trionoj de la voĉoj — two thirds of the votes
As adjectives (with -a):
duona horo — half an hour kvarona kilogramo — a quarter kilogram
A half portion: duonaĵo — half-piece, half-portion (using -aĵ- for "a concrete thing")
4. Decimals with komo
Esperanto uses a comma (komo) as the decimal separator, following continental European convention (not a point):
3,14 = tri komo unu kvar (pi) 2,5 = du komo kvin 0,75 = nulo komo sep kvin 99,9% = naŭdek-naŭ komo naŭ procentoj
5. Multipliers with -obl-
The suffix -obl- creates multiplier adjectives meaning "-fold" or "double/triple/etc.":
| Number | Multiplier | Meaning |
|---|---|---|
| du | duobla | double, twofold |
| tri | triobla | triple, threefold |
| kvar | kvarobla | quadruple, fourfold |
| dek | dekobla | tenfold |
La prezo duobliĝis. — The price doubled. (with -iĝ-) Ni triobligis nian rapidecon. — We tripled our speed. (with -ig-) Duobla kamero — double room Triobla ĉampiono — triple champion
As adverbs (-oble):
Duoble — doubly, twice as much Triоble pli malrapida — three times slower
6. Groups and Distribution with -op- and po
-op- creates words meaning "in groups of N":
| Number | Group word | Meaning |
|---|---|---|
| du | duope | in pairs, two by two |
| tri | triope | in threes |
| kvar | kvarope | in fours |
| kvin | kvinopo | a group of five |
La studentoj eniris duope. — The students entered in pairs. Ni promenis triope tra la parko. — We strolled through the park in a group of three. Kvinopo da soldatoj — a group of five soldiers
po (at the rate of, apiece, each):
Donu al ĉiu po tri pomoj. — Give each person three apples (three apiece). Ili pagis po dek eŭroj. — They paid ten euros each. Li aĉetis po kvar biletojn. — He bought four tickets each/at a time.
po answers the question "how many per person/unit?":
Ĉiun tagon mi legas po du ĉapitroj. — Each day I read two chapters (per day).
Dialogue
Two people discussing a survey result.
Lena: Vi vidis la novan enketon? La rezultoj estas surprizaj. Mika: Ne ankoraŭ. Kiom da homoj partoprenis? Lena: Proksimume du milionoj kaj kvarcent mil respondintoj el dek kvin landoj. Mika: Kaj kio estis la ĉefa trovaĵo? Lena: Laŭ la enketo, preskaŭ du trionoj de la respondintoj parolas almenaŭ unu fremdan lingvon. Mika: Kaj kiom procentoj parolas tri aŭ pli? Lena: Kvin komo sep procentoj. Tio estas proksimume centoble pli ol antaŭ dudek jaroj. Mika: Nu, ne centoble, sed sendube pli. Ĉu la rezultoj diferencas laŭ aĝo? Lena: Jes, inter junuloj ĝis dudek kvin jaroj, la proporcio estas preskaŭ duobla kompare al la pli maljuna generacio. Mika: Interese. Kaj la enketo estis farita ĉiumonate, ĉu? Lena: Jes, po kvin mil intervjuoj monate dum la lasta jaro.
Practice
Exercise 1: Write the Number in Words
Write each number as Esperanto words.
- 4,500,000
- 3/4
- 2.5
- The 21st century
- In groups of three
- Give each student 5 books
Answers:
- kvar milionoj kaj kvincent mil
- tri kvaronoj
- du komo kvin
- la dudek-unua jarcento
- triope
- donu al ĉiu studento po kvin librojn
Exercise 2: Translate the Sentence
- Half of the students passed the exam.
- The price tripled in three years.
- Two thirds of the population live in cities.
- They worked in pairs all day.
- Pi is approximately three point one four.
Answers:
- Duono de la studentoj pasis la ekzamenon.
- La prezo triobliĝis en tri jaroj.
- Du trionoj de la loĝantaro loĝas en urboj.
- Ili laboris duope la tutan tagon.
- Pi estas proksimume tri komo unu kvar.
Exercise 3: Use -obl-, -on-, -op-, po
Fill in the correct form.
- ___ pli ol hieraŭ (twice as much as yesterday): ___oble pli
- one fifth of the budget: unu ___ono de la buĝeto
- in groups of four: ___ope
- three books each: po ___ librojn
Answers: 1. Duoble 2. kvino 3. kvarope 4. tri
Cultural Note
Esperanto uses the long scale for large numbers, which is standard in most of continental Europe: miliono (10⁶), miliardo (10⁹), biliono (10¹²). This contrasts with the American/British short scale where "billion" means 10⁹. When communicating with Esperanto speakers from different countries about large numbers, it is always worth clarifying — especially in financial or scientific contexts. The Esperanto decimal comma (komo) can also catch English speakers off guard, since in English the comma is a thousands separator. These conventions reflect Esperanto's deep roots in continental European mathematical and scientific culture, and are important to internalize for reading Esperanto news, statistics, and academic texts correctly.