The number system of Common is mostly very straight-forward and regular and is reminiscient of the types of systems found in languages like Japanese and Chinese. This article will explain cardinal and ordinal numbers, use as modifiers and terms, and basic math operations.

Numbers in Common are modifiers of quantity or frequency that can be used as adjectives or adverbs. As adjectives, they count the head term; as adverbs, they specify a number of executions (like saying 'twice' or 'fivefold' in English. They are used in noun or verb phrases directly or in various roles by derivation, and are used just on their own to count.

The word for number in Common is 'tret'. It is useful in some number expressions.

There are a few number words with irregular stress marked with an acute accent. In casual writing, it is common to not use the accent and rely on the reader to know the stress.

Counting

Counting in Common is done with the base forms of the number and is very regular. Numbers are compounded from words juxtaposed in a very regular pattern. The written style is to hyphenate the numbers in a compound number. From a pronunciation standpoint, they act like separate words and not compounded words. Counting proceeds according to the following pattern:

Common borrows from American English the convention of using commas for separators to make large numbers more readable, and periods for decimal points.

A few points about numbers:

• The numbers are completely regular and never change form.
• There are no linkers like 'pi' used, and in writing, each word in a number is written separately and not compounded.
• The word for thousand has an irregular stress, and when compounded to make words for higher order number, takes the primary stress with a secondary stress on the first syllable of the word.
• Numbers of order higher than 1000 are made by taking a number word in sequence, inserting an -s- to make it ordinal, adding the suffix -areju, and then adding the suffix -n. This system lines up with the 'short scale' popular in the pre-Collapse English-speaking world (resulting in a precipitous decline in the use of the long scale globally). So short-scale sextillion is 'wanisaréjun' - both contain the word for 'six'.
• For higher-order numbers, the -n suffix is dropped when making 'count word' forms, so 'kawasaréutret', not 'kawasaréunytret'.

Decimals

Decimals are expressed in Common similarly to the way they are expressed in English, which is not a coincidence. Old Common didn't have decimals, and decimals were quickly created in the Early Period by copying the idoms of English.The word 'mora', point or dot, is used as the separator between the whole number portion of the number and the decimal portion. The decimal portion is read as just the numbers one at a time. The first five decimals of pi, for example, would be:

net mora ate akin ate suz xiro
three point one four one five nine
3.14159

Counting with Nouns

The base forms of numbers are members of the modifier class and fit in the quantity position in the modifier sequence. Numbers are tight binding modifiers, each applying to the next in sequence, except for the last in sequence, which is loose binding and applies to the head term. Together they form a compound modifier expression that acts as a single modifier. As noted when we discussed nouns, the use of a number as quantifier generally requires a paucal article. When used with a paucal, the number is construed to be exact and partitive. The paucal is required even when the number is 'cul', 'zero'. The exception is 'ate', 'one', which requires the singular. A number can be used with the plural, but in that case tends to imply a whole rather than a part, and an approximate rather than exact number. There is some grey area in these divisions which needs to be sorted out from context.

Another thing to note is that when a number is used as a quantifying modifier, it can optionally take the suffix '-no', which normally derives a tight binding modifier from a loose binding modifier. This usage arose spontaneously in the middle period to repair some situations where the number meant might be ambiguous - we will see that below when we discuss numbers as measure units.

Examples:

Na ate Onpa
One World

This is a slogan of the New World Order - the word 'ate' is emphasizing the singularity and unity of the planet. Notice the singular number is used.

Nar fosse-ate Dalmatian paluh
One Hundred and One Dalmatians

This is the title of an old cartoon screenshow. The dog breed Dalmatian is just borrowed straight into Common and pronounced as though it were spelled 'talmaxyn' by dog enthusiasts. The word 'paluh' for 'dog' is idiomatically required for most people to understand this title. Notice the paucal number is used.

Nyz atesaréjun skitrem.
A million mice

This is a relatively less common use of the plural with a number. The speaker is using the word 'atesaréjun', 'million', as an approximation to emphasize there are a lot of mice and to refer to the mice in a mass.

Statements of Number

By statements of number, we mean sentences and clauses primarily conveying how many there are of something. There are two things on particular to note. One, any time an exact number is implied, the paucal will be used, even for zero things, unless it's for for one thing, in which case the singular is used. The plural implies approximation. Two, the indefinite will usually be used, which has a partitive sense like 'some' out of some imagined possible mass of many. If the definite is used to puts the focus on these specific items in particular any not any other similar items you could have. 

Examples: 

Yr suz-naw kala se an.

There are (exactly) fifty apples.

Je te tret yr net-naw hulaz.

I am thirty [years old], literally, "I count 30 years.

Numbers as Count Units - 'Dozens', 'Hundreds', 'Thousands'

English has an idiom whereby certain numbers can be used like units of measure - taking a noun like 'bricks', for example, you could say 'thousands of bricks' just as easily as you could say 'tons of bricks'. The parallel does work with mass nouns - you could have 'tons of rice' but not 'thousands of rice', the thing measured has to be countable - but the comparison gives an idea of how the idiom in English is usually grammatically structured. Notice that only certain numbers can participate in this structure, you can have 'hundreds of bricks' but not 'eighties of bricks'.

Common has a very similar idiom using the term 'tret' as a suffix to a number to create a counting unit, much like the English 'dozen' for twelves of something or the French 'dizain' for tens of something. You would read it like 'something-count', so 'ny nawytret' is a 'ten-count', the same idea as 'dizain'.This derived term can then be counted almost like any other term, so you can have:

Nyr suzno naw-kawatret
Five dozen

Notice that if you add a number to count a unit created this way, the overall phrase must be in the paucal number, as required for anything counted exactly. Otherwise, the number is always singular. Also notice that the tight binding suffix -no is being used in this case to break up the number words next to one-another and clear up the ambiguity between 'fifty pairs' versus 'five dozen' which would be easy to confuse in speech.

If you want to specify fifty dozen of what, you add the thing being counted as a modifying phrase introduced with the null preposition. The thing being counted is always in the paucal number and tends to be definite, even as the unit is indefinite, and even if there is only one unit of it, a grammatical peculiarity that goes back to the early period and has persisted, even in Low Common. So:

Ja atuin tene pulek yr suzno naw-kawatret nar welop.
The person has bought five dozen eggs.

Any number can potentially be used as a count measure in this way, but it's much more common with certain idiomatically popular numbers - 'kawatret', or 'pair', and the multiples of ten. This is particularly so when counting units are used vaguely to give a sense of a lot of something and the type of magnitude being discussed. In this case, the plural rather than the paucal is used for the counter, but it still tends to be expressed as indefinite. The thing counted, if expressed, is still definite and in the paucal number. For example:

Ja atuin tene pulek yz fossetret nar welop.
The person has bought hundreds of eggs.

Ordinal Numbers

These are numbers like 'first', 'second', 'third', 'fifth', etc. in English that give number in a sequence. To make an ordinal in Common, an unusual derivation is used. The suffix -(y)s, which normally derives a modifer from a term, is applied to the last number word in the number expression to turn the whole expression into an ordinal. As an ordinal, the number becomes a modifier of manner in sequence.

Example:

Na net-naw-suzys pikki.
The(NOM.SG) two-ten-five-MOD cat

'The twenty fifth cat.'

Use with Verbs

Base numbers, used as an adverb, express frequency, translating expressions like 'twice', 'fivefold' or 'ten times'.

Example:

A pocuk noxot kawa zisse ija atuin.
The(ABS) child go(NP.PF) two tell the(DAT) person.

'The child has spoken with the person twice.

When an ordinal number is used to modify a verb, it translates as an adverbial expression like 'firstly' or 'secondly' - this type of usage is common in building narrative flow.

Kawas, ja pocuk hanno yn a slek ija pikki.
Two-MOD, the(ERG) child give(P.PF) TERM the(ABS) food the(DAT) cat.

'Secondly, the child fed the cat.'

Note that the term 'happat', to give, which would normally be dropped in this expression, needs to be replaced with the dummy term 'yn', as in the example above, or used explicitly, if using an adverb like 'kawas' for narrative structure. This is because 'kawas' is considered to be a modifier that belongs to the main verb, and as such triggers the mandatory head term rule when present.

Use as Nouns

To use a number as a noun, it must be derived into the term class with the suffix -(y)n. The entire number expression collectively becomes a noun and the hyphenation is maintained in writing. Such a word is typically construed as singular. Either cardinal (base form) or ordinal numbers can be derived in this way.

Cardinal: 

Conveys the idea of a group of a set number, or else the abstract idea of that number.

Examples:

Na wanin
The (group of) six.
The number six

If the derire is to make it very clear that you are talking about the number six as an abstract quality, or about a literal, written number six, the derived term can be used as a modifying term for the word 'tret', 'number':

Na wanin tret.
The number six.

Ordinal

Conveys the idea of that particular one in a sequence. If you want to specify the thing being counted, you would leave the ordinal alone and not derive it into a term, unless its ordinal number was somehow also its name, in which case deriving into a term and using as a modifying term would be appropriate to convey that idea.

Exmaple:

Na suzysyn
The fifth one.

Use as Verbs

Numbers used as verbs are derived in the same manner as for nouns, with the suffix -(y)n to turn them into terms. They convey the idea of multiplying something a set number of times (but not in the sense of the math operation on numbers, usually), or placing something at a certain place in sequence.

Cardinal: 

Conveys the idea of multiplying by the set number - translates words like 'to double' or 'to triple'. These are intransitive pali verbs with an absolutive object that is multiplied. They can be used in a causative form as skurun verbs with an ergative subject that performs the multiplication.

Examples:

Ja atuin tene netyn a slek
The person tripled the food.

A tret naz skitrem sete nawyn.
The(ABS) number (of) the(NOM.P) mouse stand(NP.PF) ten(TER)

'The number of mice has increased tenfold.'

The number 'one', 'ate', is very important in this sense, because its verbal form 'te aten' means to unite or unify. We see forms like this in the Common versions of some historic placenames, like 'Nar Atenkas Sifysyn na Myrika', 'the United States of America', or 'Na Atenysyn na Hare Jurop', 'the Northern European Union'. The latter arguably can be understood purly from the noun sense of 'aten', reading like 'one-like-ness', but the former using a thematic suffix -ka explicitly draws on the verbal sense, 'that with the quality of having been united'.

Ordinal

Conveys the idea of setting a thing at that particular place in a sequence. Ordinals converted to verbs are ditransitive happat verbs with an ergative subject that is the placer, an absolutive object that is the thing placed, and a dative indirect object which is the sequence the thing is placed in.

Exmaple:

Ja atuin hap atesyn a sy pocuk.
The(ERG) person give(NP,IM) one-MOD-TER the(ABS) sir child.

'The person places their child first.'

This is an idiomatic way of saying that any particular thing is one's top priority. Notice the adposition possessive using the polite term 'sy'. In this case the 'sy' refer's back to the person, who we are talking about in a polite and respectful way.

Fractions

There is a regular idiom for expressing fractions, and in addition, there are special, irregular words to express certain special fractions, the only irregular elements in Common's number system.

The regular pattern employs the internal conjunction 'jo', which usually means 'but'. You say the numerator, then 'jo', then the denominator. For example:

Ate jo kawa
One half

Naw-akin jo net-naw-wani
Fourteen thirty-sixths

The 'jo' is not hyphenated with the numbers. Words formed this way work much like cardinal numbers in terms of how they are used and how they can be derived into various noun and verb expressions, with some exceptions.

Quantifying something:

Nar ate jo kawa osek.
The half of a fruit.

A paucal is required for a fraction because it exactly counts something and isn't exactly one.

Referring to a portion of something:

Na ate jo akin kit
The quarter portion

A regular fraction can't be derived into a term and needs help from a head term like 'kit', 'part'.

As an adverb:

Ja pikki tene ate jo kawa slek a skitrem
The cat half ate the mouse.

In this case, the fraction specifies and quantifies an incomplete action.

Fractions cannot directly derive into terms, but a verbal sense like 'divide into X parts' can be achieved by adding a supporting head term like 'kit':

Ja atuin tene ate jo kawa kit a osek.
The person halved (cut in half) the fruit.

Ordinal forms cannot be made from fractions.

In addition, there are irregular forms that mean one half, one third and one quarter.

These words are more versatile and can directly derive into terms with meanings like 'a half part' or a skurun verb 'to divide in half'. For their specific meanings. speakers will prefer them over their regular counterparts. So in the above example, the below is more likely:

Ja atuin tene akáwasyn a osek.
The person halved (cut in half) the fruit.

Simple Math

Finally, we will address the four basic operations of arithmetic, addition, subtration, multiplication and division, and negative numbers. First, negative numbers - numbers are made explicitly positive or negative with the tight binding modifiers 'ik' (negative) and lano (positive). It is usually not necessary to use 'lano', but it can be used for clarity or emphasis. Example:

Ik naw-kinni
Negative seventeen.

The sign operator ik or lano must be placed before any of the words that make up the compound number.

The idea of an arithmetic equation is expressed with the verb 'an', to be. 'An' is used as an intransitive pali verb for this meaning, with an absolutive subject which is the arithmetic expression being evaluated and the answer as an adverb of 'an'.

To build the arithmetic expression, internal conjunctions are used to connect the numbers to be operated on and the expression forms a single noun phrase with a dummy term 'yn' to make it obey the rules of Common grammar.

The following examples show how this system comes together.

Examples:

A kinni pi net yn se an naw.
Seven and three make ten.

A kawa-naw jo suz yn se an akin.
Twenty divided by five is four.

A wani han xiro yn se an suz-naw-akin.
Six times nine is fifty-four.

A kawa han ik net yn se an ik wani.
Two times minus three is minus six.