Lesson 3: Numbers and Counting

Overview

Numbers are among the most immediately practical vocabulary in any language. From buying coffee to exchanging phone numbers to saying the year of your birth, numerals appear in daily life hundreds of times a day. Esperanto's number system is built on a small set of roots that combine with perfect regularity to produce every number from zero to infinity. There are exactly ten basic numeral roots, and once you know them, you can construct any number you need by simple combination — no irregular forms, no special rules for "teens," no unexpected changes.

This lesson also introduces two productive grammatical mechanisms: ordinal numbers (formed by adding the adjective ending -a to any numeral) and fractions (formed with the suffix -on-). Together, these three systems — cardinal, ordinal, and fractional — give you the full mathematical vocabulary needed for A1 communication, from telling the time to describing dates to talking about quantities.

Learning Objectives

By the end of this lesson you can:

• Count from 0 to 1,000,000 using the ten basic numeral roots
• Form any ordinal number (first, second, third…) with the -a ending
• Express fractions (half, third, quarter…) using the -on- suffix
• State that Esperanto cardinal numbers are invariable (no plural or accusative)
• Use numbers in practical contexts: phone numbers, ages, prices, dates

Vocabulary

Esperanto	Type	English	Example sentence
nulo	numeral	zero	La temperaturo estas nulo gradoj.
unu	numeral	one	Mi havas unu fraton.
du	numeral	two	La tablo havas du krurojn... ne, kvar.
tri	numeral	three	Tri kaj tri estas ses.
kvar	numeral	four	La jaro havas kvar sezonojn.
kvin	numeral	five	Mi havas kvin fingrojn sur ĉiu mano.
ses	numeral	six	La semajno havas ses labortagnojn.
sep	numeral	seven	La semajno havas sep tagojn.
ok	numeral	eight	Ok kaj du estas dek.
naŭ	numeral	nine	Naŭ minutoj restas.
dek	numeral	ten	Mi havas dek fingrojn.
dudek	numeral	twenty	Li havas dudek jarojn.
tridek	numeral	thirty	La kurso kostas tridek eŭrojn.
cent	numeral	hundred	Cent homoj venis al la kongreso.
mil	numeral	thousand	Mil jaroj estas jarmilo.
miliono	numeral	million	Ses milionoj da homoj parolas Esperanton.
nombro	noun	number	Kio estas via telefona nombro?
kalkuli	verb	to count, calculate	Mi ne povas kalkuli rapide.
aldoni	verb	to add	Aldonu du kaj tri.
subtrahi	verb	to subtract	Subtrahu kvin el dek.
duono	noun	half	Duono de dek estas kvin.
triono	noun	third (fraction)	Triono de naŭ estas tri.
kvarono	noun	quarter	Kvarono de horo estas dek kvin minutoj.
unua	adjective	first	La unua leciono estas facila.
dua	adjective	second	La dua lingvo estas pli malfacila.
tria	adjective	third	La tria sekcio estas interesa.
aĝo	noun	age	Kian aĝon vi havas? Mi havas dudek jarojn.
prezo	noun	price	Kio estas la prezo?

Grammar Focus

Pattern 1: Building Any Cardinal Number

Structure: [tens] + [units], combined as one word or with hyphen

Esperanto cardinal numbers are built by simple juxtaposition. The tens (dudek, tridek, kvardek, kvindek, sesdek, sepdek, okdek, naŭdek) are formed by adding -dek to the digit roots. For compound numbers, you write the larger unit first, then the smaller: dudek unu (21), tridek ok (38), cent kvardek du (142). Hundreds are formed by adding cent: ducent (200), tricent (300). Thousands use mil: du mil (2,000), tri mil kvarcent (3,400).

Crucially, Esperanto numerals are invariable: they never take the plural ending -j and never take the accusative ending -n. This is in contrast to nouns and adjectives. You say tri libroj (three books) — the noun gets the plural -j, but tri stays as tri.

Number	Esperanto	Notes
11	dek unu	"ten one"
15	dek kvin	"ten five"
21	dudek unu	"twenty one"
55	kvindek kvin	"fifty five"
100	cent	stand-alone
200	ducent	du + cent
1,000	mil	stand-alone
1,500	mil kvincent	mil + kvincent
1,000,000	miliono	stand-alone noun

Common mistake: Adding -j to numerals → ❌ "trij libroj" → ✓ "tri libroj" (only the noun takes plural -j)

Pattern 2: Ordinal Numbers with -a

Structure: numeral root + -a = ordinal adjective

Ordinal numbers in Esperanto are formed by adding the adjective ending -a to the cardinal number. This is completely regular: unu → unua (first), du → dua (second), tri → tria (third), and so on without any irregularity (compare English: one/first, two/second, three/third — all irregular). Because ordinals are adjectives, they follow the normal adjective rules: they take -j in the plural and agree with the noun they modify.

Cardinal	Ordinal	English	Example
unu	unua	first	La unua leciono estas facila.
du	dua	second	La dua tago de la semajno estas mardo.
tri	tria	third	Li loĝas en la tria etaĝo.
dek	deka	tenth	La deka de januaro estas mia naskiĝtago.
dudek	dudeka	twentieth	La dudeka jarcento estis tre grava.

Common mistake: Using cardinal instead of ordinal for dates and order → ❌ "La du leciono" → ✓ "La dua leciono"

Pattern 3: Fractions with -on-

Structure: numeral root + -on- + noun ending -o = fraction noun

Fractions are formed by inserting the suffix -on- between the numeral root and the noun ending -o. This suffix means "one part in [number]": du + -on- + -o = duono (a half), tri + -on- + -o = triono (a third), kvar + -on- + -o = kvarono (a quarter). The system extends to any number: dek-duono would be a twelfth, cento would be... well, centono (a hundredth). These fraction nouns behave like ordinary nouns and can take -j (plural) and -n (accusative) as needed.

Fraction	Esperanto	Example sentence
1/2	duono	Unu duono de dek estas kvin.
1/3	triono	Manĝu nur trionon de la kuko.
1/4	kvarono	Unu kvarono de horo estas dek kvin minutoj.
3/4	tri kvaronoj	Tri kvaronoj de la studento lernas bone.
1/5	kvino / kviono	Kviono de la grupo parolas Esperante.

Common mistake: Confusing du (two) and duono (half) → ❌ "Donu al mi du da teo" (give me two of tea, nonsensical) → ✓ "Donu al mi duonon da teo" (give me half of the tea)

Dialogue

At an Esperanto congress registration desk

— Bonan tagon! Mi volas registriĝi. — Good day! I would like to register.

— Bonan tagon! Kio estas via nomo? — Good day! What is your name?

— Mi nomiĝas Yuki Tanaka. T-A-N-A-K-A. — My name is Yuki Tanaka. T-A-N-A-K-A.

— Dankon. Kian aĝon vi havas, sinjorino Tanaka? — Thank you. How old are you, Ms. Tanaka?

— Mi havas dudek ok jarojn. — I am twenty-eight years old.

— Kaj kio estas via telefona nombro? — And what is your telephone number?

— Naŭ, tri, kvin, du, ok, unu, sep, kvar. — Nine, three, five, two, eight, one, seven, four.

— Perfekte. La kongreso komenciĝas la dudek kvina de julio. — Perfect. The congress begins on the twenty-fifth of July.

— La dudek kvina? Tio estas post morgaŭ! — The twenty-fifth? That's the day after tomorrow!

— Jes! La unua sesio estas je la naŭa horo matene. — Yes! The first session is at nine o'clock in the morning.

— Bone. Kiom kostas la aliĝkotizo? — Good. How much does the registration fee cost?

— Cent kvindek eŭrojn. Aŭ okdek eŭrojn por studentoj. — One hundred and fifty euros. Or eighty euros for students.

Practice

Exercise 1: Fill in the blank

Write the Esperanto number.

1. 7 = ___
2. 13 = ___
3. 45 = ___
4. 100 = ___
5. 1,000 = ___

Exercise 2: Translate to Esperanto

1. I am thirty-two years old.
2. The second lesson is more difficult.
3. Give me half of the bread, please.
4. The congress has three thousand participants.
5. The first day of the week is Monday.

Exercise 3: Questions to answer in Esperanto

1. Kian aĝon vi havas?
2. Kiom da tagoj havas la semajno?
3. Kio estas duono de dudek?

Cultural Note

At international Esperanto events — particularly the annual Universala Kongreso, which has been held every year (except during the World Wars) since 1905 — numbers take on special social significance. The congress number is always announced with pride: "La 109-a Universala Kongreso!" where 109-a uses exactly the ordinal-number rule from this lesson. Participants often introduce themselves by mentioning how many years they have spoken Esperanto, turning a simple number exchange into a measure of commitment to the movement.

Esperanto also has a rich tradition of word games and puzzles that rely on the composability of its number roots. The suffix -op- (not taught at A1 level but worth knowing exists) creates collective numbers: duope means "in pairs/twos," triope means "in threes." This kind of systematic derivation delights mathematically minded learners and demonstrates why many scientists, engineers, and logicians have been drawn to Esperanto throughout its history — the language rewards the same systematic thinking that makes mathematics accessible across cultures.