Convert decimal numbers to ternary (base3) with clear step-by-step derivation
Decimal Number
Result
Base3 (Ternary) Result
Step-by-Step Derivation
Decimal to Base3 Conversion Principle
① Integer part: Repeated division by 3, collect remainders
② Fractional part: Repeated multiplication by 3, extract integers
③ Read remainders from last to first for integer part
Base3 (ternary) is a fascinating number system with elegant mathematical properties, historically used in computing experiments.
⚠This converter supports both integer and fractional decimal numbers. Maximum fractional precision is 10 digits in base3.
What Is Base3 (Ternary)?
Base3 (ternary) is a positional numeral system with base 3. Standard ternary uses digits 0, 1, and 2, while balanced ternary uses T, 0, and 1 for -1, 0, and +1.
Mathematical Efficiency
Base e (~2.718) is theoretically optimal. Base3 is the closest integer, making it very efficient for information representation.
Historical Computing
The Setun computer, built in the Soviet Union in 1958, used balanced ternary logic and was successful!
Balanced Ternary
Balanced ternary uses -1, 0, +1. No sign bit needed! It allows elegant arithmetic and representation.
Digit Values
In standard ternary: 0=0, 1=1, 2=2. Each position represents a power of 3 (3^0, 3^1, 3^2, etc.).
Computer ScienceNumber TheoryMathematicsEducationRecreational Math
Frequently Asked Questions
What is base3 (ternary)?▼
Base3 or ternary is a positional numeral system with base 3. It uses three digits: 0, 1, and 2. Balanced ternary uses -1, 0, and +1, often represented as T, 0, and 1.
How do you convert decimal to base3?▼
To convert decimal to base3, repeatedly divide the number by 3 and collect the remainders. The remainders, read from last to first, give the base3 number. For fractional parts, multiply by 3 repeatedly.
What are the advantages of base3?▼
Mathematically, e (~2.718) is the most efficient base for information storage. Base3 is the closest integer, making it very efficient. Historically, the Setun computer used balanced ternary!
How do you convert fractional decimal to base3?▼
For fractional parts, multiply by 3, extract the integer part as a base3 digit, and repeat with the remaining fraction until sufficient precision or termination.
Free online calculators and tools covering mathematics, unit conversion, text processing, and daily life. Accurate, fast, mobile-friendly, and completely free to use.