Editing Balanced ternary (section)

=== Other applications ===
The theorem that every integer has a unique representation in balanced ternary was used by [[Leonhard Euler]] to justify the identity of [[formal power series]]<ref>{{cite journal
 | last = Andrews | first = George E.
 | doi = 10.1090/S0273-0979-07-01180-9
 | issue = 4
 | journal = Bulletin of the American Mathematical Society
 | mr = 2338365
 | pages = 561–573
 | series = New Series
 | title = Euler's "De Partitio numerorum"
 | volume = 44
 | year = 2007| doi-access = free
 }}</ref>
:<math>\prod_{n=0}^{\infty} \left(x^{-3^n}+1+x^{3^n}\right)=\sum_{n=-\infty}^{\infty}x^n.</math>

Balanced ternary has other applications besides computing. For example, a classical two-pan [[Weighing scale#Balance|balance]], with one weight for each power of 3, can weigh relatively heavy objects accurately with a small number of weights, by moving weights between the two pans and the table. For example, with weights for each power of 3 through 81, a 60-gram object (60<sub>dec</sub> = 1T1T0<sub>bal3</sub>) will be balanced perfectly with an 81 gram weight in the other pan, the 27 gram weight in its own pan, the 9 gram weight in the other pan, the 3 gram weight in its own pan, and the 1 gram weight set aside.

Similarly, consider a currency system with coins worth 1¤, 3¤, 9¤, 27¤, 81¤. If the buyer and the seller each have only one of each kind of coin, any transaction up to 121¤ is possible. For example, if the price is 7¤ (7<sub>dec</sub> = 1T1<sub>bal3</sub>), the buyer pays 1¤ + 9¤ and receives 3¤ in change.