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Part I: Esperanto Grammar

9. Numbers & Measurement

The following Esperanto roots function as numbers:

1 = unu
2 = du
3 = tri
4 = kvar
5 = kvin
6 = ses
7 = sep
8 = ok
9 = naŭ
ten = dek
hundred = cent
thousand = mil

Each of these may be used directly before a noun as a number:

tri francaj kokinoj = three French hens
kvin oraj ringoj = five golden rings
mil dancistinoj = a thousand dancing girls

The elements may be combined to produce remaining numbers between 10 and 999,999 in a way comparable to the way in English we say “two thousand three hundred six.”

*-To distinguish years from other numbers, many Esperanto speakers say la jaro before the year number: Mi naskiĝis en la jaro 1967. = “I was born in 1967.” Occasionally one finds the abbreviation j. written after a year, even though it does not correspond with a spoken form: Mi naskiĝis en 1967 j. = “I was born in 1967.”

tridek = 30
tricent dek = 310
kvardek kvin = 45
dumil tricent ses = 2,306
trimil sepcent kvindek ok = 3,758
mil sepcent naŭdek ok = 1798*

In writing, one links together two elements when one is the multiplier of the other. Thus the units that stand separately are usually added to each other to make the whole number:

mil naŭcent naŭdek ok = 1998
1000 + (9x100) + (9x10) + 8 = 1998

Since only two elements may be written together, it sometimes happens with large numbers that a long string of items in fact multiplies the next unit:

ducent tridek kvin mil = 235,000
(200 + 30 + 5) x 1000 = 235,000

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9.1. Numbers as Nouns

*-“Dozens of people” is literally dekduoj da homoj, but given the arrangement of Esperanto numbers to the base ten, such an expression comes across as weirdly English. It is better to say dekoj da homoj even if the English would be “dozens of people.” (Measuring in dozens, or for that matter tens or scores, is after all a cultural convention, not a mathematical necessity.)

Numbers higher than 999,999 have a slightly different form because the words miliono = “million” and miliardo = “billion” are nouns. One says mil homoj = “a thousand people” but miliono da homoj = “a million people.” (See the article on biliono in Part II.)

Regular numbers, by the addition of -o, can also become nouns in order to say things like “tens of people” = dekoj da homoj or “hundreds of refrigerators” = centoj da glaciŝrankoj.* 1

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9.2. Decimal Points

In Asia and North America we use a period for a decimal point and a comma to set off numbers in groups of three: 12,344.56. In Europe a comma is commonly used to represent a decimal point, and a small space (or occasionally a period) is left where we would put the comma: 12 344,56 or 12.344,56. In Britain a period is used to represent the decimal point, just as we do, but it is often raised slightly in printing and handwriting. Most Europeans are aware of American usage (which is increasingly being adopted internationally), but usage in Esperanto varies. Do as you please -I myself follow American usage in this- but be prepared for anything. In reading out numbers, a comma is komo and a period punkto, wherever they are placed.

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9.3. Ordinal Numbers

The addition of the adjective suffix -a to numbers produces ordinal numbers:

unu = one unua = first
du = two dua = second
tri = three tria = third
naŭ = nine naŭa = ninth
kvardek du = 42 kvardek dua = 42nd
cent tridek = 130 cent trideka = 130th

The usual written abbreviation appends the letter -a (sometimes alone, sometimes with a hyphen, and sometimes raised slightly) to the Arabic numeral: 9a, 9-a, 9a, 130a, 130-a, 130a. The form with the hyphen is commonest.

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9.4. Arithmetic

The following examples provide guidance on common operations in arithmetic:

tri plus kvin estas ok = 3+5=8
kvin minus tri estas du = 5-3=2
trioble kvin estas dek kvin = 3x5=15
dek kvin dividite per kvin estas tri = 15÷5=3
kvinone dek kvin estas tri = 15÷5=3

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9.5. Fractions

Fractions are made in Esperanto with the suffix -on-.

tri kvaronoj = three-quarters
duono = half, a half, one-half
kvar kvinonoj = four-fifths
sep sesonoj = seven-sixths
unu ducent sepdek kvinono = 1/275th
duonkilogramo = half a kilo, one-half kilo, half of a kilo
kvaronlitro = quarter of a liter, quarter liter, one-quarter of a liter
duono da kilogramo half a kilo, one-half kilo, half of a kilo

Caution: Occasional fractions are ambiguous:

cent dek duonoj = 100/12 OR 110/2

In speaking it is necessary to resolve the ambiguity by intonation and pace of speech. In writing, one can simply hyphenate the elements that go together:

cent dek-duonoj = 100/12
cent-dek duonoj = 110/2

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9.6. Time

The most common way of telling time in Esperanto is to express the number of minutes or the fraction of an hour that falls before or after an hour; the hours themselves are called the 7th, the 3rd, and so on, sometimes with the word horo = “hour,” sometimes not:

la sepa (horo) = 7 o’clock
kvin minutoj post la sepa = five after seven
la sepa kaj dudek = seven twenty
dudek kvin antaŭ la kvina = twenty-five minutes to five
kvarono antaŭ la dekdua = quarter to/of twelve
Estas jam la kvina! = It’s already five o’clock!
Kioma horo estas nun? = What time is it now?

Caution: Many languages have expressions such as our “a quarter of eight.” However, in some languages “a quarter of eight” means 7:45; in others it means 8:15! Esperanto has no such expression, but should you hear a faltering speaker try to make one, try to elicit the information again in standard format. Otherwise, you may miss the appointment!

Because the ordinal (e.g., la sepa) is used to refer to the hour of the day, asking the time requires using kioma, since that is the question-word that demands an ordinal number in response. (See the section on correlatives.)

Kiom da horoj ni atendis? Sep. = How many hours did we wait? Seven.
Kioma horo estas? La sepa. = What time is it? Seven.
Kioman tagon li venos? La sepan. = What day will he come? The seventh.
Kiam li venos? Je la sepa. = When will he come? At seven.
Kiun tagon li venos? Mardon. = Which day will he come? Tuesday.

At the heading of a letter the date may be written out in full as follows: dimanĉon, la 17-an de marto 2013 = “Sunday, March 17, 2013.” The day name and date number are in the accusative to show that the letter is written on that date.

When abbreviations are used, international usage varies. The American custom of shortening dates by writing, for example, 3/15/13 to mean March 15, 2013, is universally regarded as illogical outside of North America, since it puts the smallest unit (days) in the middle (reflecting the way one speaks the date in American English). In the rest of the world one progresses from the largest to the smallest or (less commonly) the smallest to the largest:*

*-A form that places the year first has the advantage that it makes date order correspond with numerical order, largest units first, smaller ones afterward. This facilitates sorting, especially by machine.

USA: 3/17/13
Western Europe: 17.3.13
China: 130317
Japan, Eastern Europe: 2013.3.17
Eastern Europe: 2013.III.17

Things have become more confusing with the year 2000, since the year numerals look like day and month numbers. (What date is 11/6/9?)

*-Then again I suppose you could also write Festo de Sankta Patriko = “St. Patrick’s Day”!

Recommendation: The International Organization for Standardization recommends the form 2013-3-17. This (or the similar 2013.3.17) is becoming most common among Esperantists and is to be recommended, but you should be prepared for anything. You should avoid the parochially American format 3/17/13. If there is any doubt about whether another person will understand, write out the full date: la 17-an de marto 2013. Remember that month names are not capitalized.*

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9.7. Monarchs

*-The French style is simpler, but present trends clearly favor the long-term triumph of the English style.

Monarchs’ names with numbers (John XXIII, Richard III) are usually read as ordinal numbers, as in English: Johano la dudek tria, Rikardo la tria. Less commonly, however, they may be read as cardinal numbers, as in French (Johano dudek tri, Rikardo tri).*

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9.8. Quantities of Things

Esperanto uses the prepositions el, de, and da when speaking of quantities that are not directly counted. (El and de also have other uses.)

El is used when one wishes to differentiate some individuals out of a group:

ses studentoj = six students
ses el la dek studentoj = six out of the ten students
tri el tiuj tasoj = three of those cups
nur mil el la tuta grupo = only a thousand from the entire group

Da is used between two words when the first is a noun naming the unit of measurement for the second:

kilogramo da teo = kilo of tea
botelo da vino = bottle of wine
skatolo da bombonoj = box of candies
guto da mielo = drop of honey
maro da mizeroj = sea of troubles
taso da kafo = cup of coffee
kapo da zorgoj = headload of worries
brakpleno da libroj = armload of books
ĉambro da studentoj = roomful of students

or with an adverb indicating the quantity

multe da mono = a lot of money
iom da akvo = some water

*-This custom seems (to me) to derive from the feeling that, as soon as the modifier is introduced, one is no longer exclusively concerned with the unit of measurement, and attention is shifted to (or shared by) the thing being measured.

If one specifies which instance of the second thing the first is intended to measure, then the da becomes de. As a practical matter, this means da becomes de before la, before correlatives, and before adjectives:*

kilogramo de tiu teo = kilo of that tea
sako de la faruno = sack of the flour
skatolo de liaj bombonoj = box of his candies
sumo de tri dolaroj = sum of three dollars
brako de bibliotekaj libroj = armload of library books

The effect of specificity can be created by the difference between da and de themselves, even without a word like la or tiu:

botelo da lakto = bottle of milk (quantity)
botelo de (la) lakto = bottle of (the) milk (object)

Remember that de can also indicate possession:

ĉambro da studentoj = roomful of students
ĉambro de studentoj
= room that belongs to students, room for the use of students
ĉambro de la studentoj = roomful of the students
OR room that belongs to the students (normally the latter)

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9.8.1. More about Da

Da may be used with plural nouns, as some of the examples here show. Accordingly the distinction is NOT the one we know in English between count and mass nouns. However the association of da with things that cannot easily be counted (like tea and flour) gives it a clear implication of things being taken as a unit, bunch, lump, or glob:

grupo de studentoj = group of students
(the group is made up of students)
grupo da studentoj = gaggle of students
(the number of students is one grupo)

As in English, this may be used to produce picturesque effects:

du instruistoj da studentoj = two teachers’ worth of students s
kafejo da laboristoj = a café-load of workmen s
tuta universitato da pajacoj = a whole university of clownss
jubilo da alaŭdoj = an exaltation of larks

In informal spoken Esperanto, a forceful turn of phrase sometimes changes the word order:

Venis policanoj, granda grego da!
= Policemen came, a whole bunch of them!

In ordinary conversation, however, the most common use of da is with the elements kelk- = “some,” mult- = “many, much,” with tro = “too (much)” and pli = “more,” and with the correlatives ending with -iom = “amount”:

kelkaj studentoj = some students, a few students s
iom da studentoj = a group of students, some students s
kelkaj studentoj = some students, a few students s
kelke da studentoj = a group of students, a few students s
kelkaj el la studentoj = a few of the students s
multaj studentoj = a lot of students, many students s
multe da studentoj = a whole lot of students, a bunch of students s
multaj el la studentoj = many of the studentss
multa mono = a lot of money s
multe da mono = a lot of money s
kiom da mono = how much money s
iom da mono = some money
Daĉjeto ĉiam deziris pli da ludiloj.
= Little Davey always wanted more toys.
Daĉjeto ĉiam deziris pli multajn ludilojn.
= Little Davey always wanted more toys.
Li kredis, ke ne eblas havi tro da ludiloj.
= He believed, that it was impossible to have too many toys.
Li kredis, ke ne eblas havi tro multajn ludilojn.
= He believed, that it was impossible to have too many toys.

In general, kelke and multe are used with da before a singular noun (multe da mono = “lots of money”). The forms kelkaj and multaj are used with plural nouns (multaj studentoj = “lots of students”). There is a good deal of variation both ways, however. Some of the variation is meaningful and really does use da to indicate groups, bunches, lumps, globs, and clots. But some of it arises from the mere habit of saying multe da so often that people forget about multa and multaj (or kelka and kelkaj).

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