135. Cardinals and Ordinals have the following uses.
a. In numbers below 100, if units precede tens, et is generally inserted.
duo et vīgintī
Otherwise, et is omitted.
b. In numbers above 100 the highest denomination generally stands first, the next second, etc., as in English. Et is either omitted entirely, or stands between the two highest denominations.
mīlle (et) septingentī sexāgintā quattuor 1764
Note— Observe the following combinations of numerals with substantives:
ūnus et vīgintī mīlitēs or vīgintī mīlitēs (et) ūnus 21 soldiers
duo mīlia quīngentī mīlitēs 2500 soldiers or
duo mīlia mīlitum et quīngentī 2500 soldiers
mīlitēs mīlle ducentī trīgintā ūnus 1231 soldiers
c. After mīlia the name of the objects enumerated is in the genitive.
duo mīlia hominum two thousand men1
cum tribus mīlibus mīlitum with three thousand soldiers
mīlia passuum tria three thousand paces (three miles)
d. For million, billion, trillion, etc., the Romans had no special words, but these numbers were expressed by multiplication (cf. § 138.a).
e. Fractions are expressed, as in English, by cardinals in the numerator and ordinals in the denominator. The feminine gender is used to agree with pars expressed or understood.
duae septimae (sc. partēs) two-sevenths
trēs octāvae (sc. partēs) three-eighths
One-half is rendered dīmidia pars or dīmidium.
Note 1— When the numerator is one, it is omitted and pars is expressed.
tertia pars one-third
quārta pars one-fourth
Note 2— When the denominator is one greater than the numerator, only the numerator is given.
duae partēs two-thirds
trēs partēs three-fourths, etc.
Note 3— Fractions are also expressed by special words derived from as (a pound).
triēns a third
See § 637.