Esper/Numbers/Big Numbers/Scientific Number Naming
This page explains an alternative system of number naming in the Esper' language which is based specifically on scientific notation.
The base is assumed to be ten unless explicitly working an another base system, in which case it is up to the writer or speaker to clarify. The exponent is placed first in the number name, with a suffix and ending a'a attached, followed by a string of digits with the first digit of the coefficient assumed to be in the one's place just before an implied decimal point rather than having to explicitly express the position of the decimal point. Note that the first digit in the coefficient should generally be non-zero, but if it is a zero, that zero is assumed to be in the one's place of the coefficient.
Here are a few examples, starting with the number we were just talking about:
tridek' sesa'a sep' nul' kvar' nul' naw' = (seven trillion forty billion nine hundred septillion) = (7.0409 * 10^36).
nula'a tri' du' = (three point two) = (3.2 * 10^0).
negdua'a kvar' tri' kvin' = (point zero four three five) = (4.35 * 10^-2).
negses' deka'a kvar' tri' kvin' = (four point three five times ten to the negative sixtieth power) = (4.35 * 10^-60).
ona'a sep' nul' du' = (seventy point two) = (7.02 * 10^1).
ona'a on' du' kvin' = (twelve point five) = (1.25 * 10^1).
If no coefficient is expressed, it is assumed to be the number one.
In this system, one googol can be expressed simply as as heka'a.
heka’a = (googol) = (10^100).
Alternatively, the prefix il' can be placed at the beginning of the number to be raised to the given power, and after the exponent which specifies to what power it will be raised, allowing hek' ildek' as another way of writing or saying the hundredth power of ten.
hek ildek' = (googol) = (10^100).
Notice that this generalized form does not allow a coefficient to be represented by a trailing string of digit names as the a'a form does, but allows any number to act as the base being raised to an exponent rather than assuming it to be ten. A coefficient can be prepended by using the suffex 'ek to mark the one's place digit in the coefficient, and following the coefficient with tce' before the corresponding base and exponent are specified.
For those who wish to deal with crazy big numbers, there is also the option of combining this generalized exponential number naming with normalized scientific notation by placing the normalized scientific notation ending last.
sepek' nul' kvar' nul' naw' tce' tridek' ses' ildeka'a du' kvin' = (two point five times ten to the seven trillion forty billion nine hundred septillionth power) = ( 2.5 * 10^7040900000000000000000000000000000000).
This would make a googolplex hek' ildeka'a (10^(10^100)) so therefore:
du' hek’ ildeka’a = (10^(10^200)).
tri' hek’ ildeka’a = (10^(10^300)).
tri' hek’ ildeka’a tri kvar kvin = 3.45 * (10^(10^300)).
Notice that the multiplier du or tri at the beginning of these examples is being applied to the higher order exponent hek and not to directly to the coefficient nor to the lower order exponent dek.
In other words, kvindek' ilheka'a (10^(100^50)) or dudek' kvin' ildek kila'a (10^(10000^25)) would also represent a googolplex.
See the page on Big Numbers for more details on the generalized exponential number naming.
See the Numbers page for more information about Esper' number naming in general.