Chapter 18: lojbau mekso: Mathematical Expressions in Lojban

3. Signs and numerical punctuation

The following cmavo are discussed in this section:

ma'u    PA  positive sign
ni'u    PA  negative sign
pi  PA  decimal point
fi'u    PA  fraction slash
ra'e    PA  repeating decimal
ce'i    PA  percent sign
ki'o    PA  comma between digits

A number can be given an explicit sign by the use of “ma'u” and “ni'u”, which are the positive and negative signs as distinct from the addition, subtraction, and negation operators. For example:

✥3.1  ni'u pa
negative-sign 1
-1

Grammatically, the signs are part of the number to which they are attached. It is also possible to use “ma'u” and “ni'u” by themselves as numbers; the meaning of these numbers is explained in c18-§8.

Various numerical punctuation marks are likewise expressed by cmavo, as illustrated in the following examples:

✥3.2  ci pi pa vo pa mu
three point one four one five
3.1415

(In some cultures, a comma is used instead of a period in the symbolic version of ✥3.2; “pi” is still the Lojban representation for the decimal point.)

✥3.3  re fi'u ze
two fraction seven
2/7

✥3.3 is the name of the number two-sevenths; it is not the same as “the result of 2 divided by 7” in Lojban, although numerically these two are equal. If the denominator of the fraction is present but the numerator is not, the numerator is taken to be 1, thus expressing the reciprocal of the following number:

✥3.4  fi'u ze
fraction seven
1/7

✥3.5  pi ci mu ra'e pa vo re bi mu ze
point three five repeating one four two eight five seven
.35142857142857...

Note that the “ra'e” marks unambiguously where the repeating portion “142857” begins.

✥3.6  ci mu ce'i
three five percent
35%

✥3.7  pa ki'o re ci vo ki'o mu xa ze
one comma two three four comma five six seven
1,234,567

(In some cultures, spaces are used in the symbolic representation of ✥3.7; “ki'o” is still the Lojban representation.)

It is also possible to have less than three digits between successive “ki'o”s, in which case zeros are assumed to have been elided:

✥3.8  pa ki'o re ci ki'o vo
one comma two three comma four
1,023,004

In the same way, “ki'o” can be used after “pi” to divide fractions into groups of three:

✥3.9  pi ki'o re re
point comma two two
.022

✥3.10   pi pa ki'o pa re ki'o pa
point one comma one two comma one
.101012001