**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.

**vīgintī duo**

** 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 men^{1}

**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

**bēs** two-thirds

See § **637**.