The Arabic Number System: Base-10
The D'ni number system is very different from the one we're used to. In our Arabic system, we can count up from zero to nine with single digits. To count higher than nine, we need two digits. The digit in the tens place tells us how many times we've cycled zero through nine, that is how many times ten is in the number, while the digit in the units place tells us where we are in the current cycle of zero through nine. Once we've hit ninety-nine, to count higher, we need a third digit for hundreds; then a fourth for thousands; and so on. This number system that we're used to is called base-10 — that is, each place in a number is ten times larger than the previous one. The tens place is ten times bigger than the units (10 = 10 x 1), the hundreds place ten times bigger than the tens (100 = 10 x 10), the thousands place ten times bigger than the hundreds (1000 = 100 x 10), and so on. For a practical example, let's look at the number 9017.
We see that each place is ten times larger than the previous one. The digit that is in each place tells us how many times that place occurs in the number: there are 9 thousands, 0 hundreds, 1 ten, and 7 units. When we multiply out (as in the diagram) and then add together, we get the number itself: 9000 + 000 + 10 + 7 = 9017.
The D'ni Number System: Base-25
Unlike our Arabic system, D'ni uses a base-25 numbering system. This means that each place in a number is not ten but twenty-five times bigger than the previous one. To illustrate like we did with Arabic numbers, we start with 1 , 1. If we increase the number so that it requires two digits, 10 (0 is the D'ni number for zero), this new number is not equal to 10, as we would think within the Arabic system; the newly introduced place is twenty-five times bigger than the previous one, 25 x 1 = 25. Thus, the D'ni number 10 is equal to 25 in Arabic terms. Introduce a third place, 100 , and it's twenty-five times bigger than the second, twenty-fives place: 25 x 25 = 625. Introduce a fourth, 1000 , and it's twenty-five times bigger yet again: 625 x 25 = 15,625. And so on.
Since D'ni is base-25, that must also mean that there are twenty-five basic digits to work with, the same way there are ten basic digits (0 through 9) in base-10. These D'ni digits are:
Let's look at a practical example, like the one above:
We now see that in D'ni, each place is not ten but twenty-five times larger than the previous one. As with Arabic numbers, the digit in each place tells us how many times that place occurs in the number: there are 9 fifteen-six-twenty-fives, 0 six-twenty-fives, 1 twenty-five, and 7 units. If we multiply out and add together as we did before, we get the value (in Arabic terms) of this D'ni number: 140,625 + 0000 + 25 + 7 = 140,657.
In transliteration, we usually represent these D'ni numbers between square brackets, with each digit separated by a vertical bar: [9 | 0 | 1 | 7].
D'ni Number Words
In English, every number can be written out with words; so too in D'ni, in a pattern that closely mirrors the logic that undergirds the number system. The numbers 0 through 4 are all simple words:
Multiples of five are also simple words:
To fill in the numbers in between, we abbreviate the word for the closest but not exceeding multiple and combine it with the word for one through four. Thus, the number six ( 6 ) breaks down into the closest multiple five plus one, vat plus fah: vagafa (vahgahfah | vagafa). (The ga means and, thus the word literally means five-and-one.) Similarly, the number fourteen ( $ ) breaks down into the closest multiple ten plus four, nAvU plus tor: nAgator (naigahtor | négator); and twenty-two ( \ ) is twenty plus two, riS plus brE: rigabrE (rihgahbree | rigabrí).
Find below a table of the D'ni numbers from 1 through | for quick reference (| is an alternative way of writing 10 , 25, when the number carries a special significance):
D'ni Numbers Larger Than 24
When we write numbers larger than nine in English, we indicate the place of each digit in words: four thousand eight hundred and ninety three. In similar fashion, D'ni uses suffixes to indicate a digit's place. These suffixes are:
Thus, the D'ni number for twenty-five ( 10 ) is a fa in the twenty-fives place: fasE. (Note that we never write out the 0 .) Three hundred twenty-five ( #0 ) is a nAgasen in the twenty-fives place: nAgasensE. We can also write out numbers with digits in both places — one hundred twenty-one ( 4] ) is a tor in the twenty-fives place and a rigafa in the units place: torsE rigafa.