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Balanced ternary is a type of numbering system with a base of 3.
The most common numbering system in use today is decimal. Decimal has a base of ten, so it has 10 digits: 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9. Ternary has a base of three, so it has only 3 digits: 0, 1 and 2. Balanced ternary also has a base of three, but it uses the digits -1, 0 and 1.
Like decimal, balanced ternary uses a place value system. Each place value is equal to the previous place value multiplied by the base. In decimal, we have a one's place, a ten's place, a hundred's place, a thousand's place, and so on. In balanced ternary, we have a one's place, a three's place, a nine's place, a twenty-seven's place, and so on.
Balanced ternary allows you to write numbers less than zero without needing a dedicated minus sign; if the digit with the biggest place-value is negative, the entire number is negative. Another benefit is that when it comes to computers, there are much fewer rounding errors.