Convert base-9 to base-20 Online | Free numbers Converter

Number System

The base-9 number system, also called the nonary system, is a positional numeral system that uses nine digits: 0, 1, 2, 3, 4, 5, 6, 7, and 8. Each digit’s position represents a power of 9, starting from $9^0$ at the rightmost digit and increasing to the left. For example, the base-9 number 357 represents $3 \times 9^2 + 5 \times 9^1 + 7 \times 9^0 = 243 + 45 + 7 = 295$ in decimal. Base-9 is useful in mathematics for exploring alternative numeral systems, positional notation, and patterns in numbers. While it is not commonly used in everyday applications or computing, it provides a unique perspective on arithmetic operations, divisibility, and number representation beyond the decimal system. Studying base-9 helps learners understand how positional systems work, how numbers can be converted between bases, and how different bases affect fraction representation and arithmetic properties. It is also valuable in theoretical mathematics and educational exercises, allowing students to develop logical thinking and problem-solving skills. Understanding the nonary system enriches knowledge of number systems and provides a foundation for exploring higher-level mathematics, coding theory, and abstract numeral systems.

-20 Number System

The base-20 number system, also called the vigesimal system, is a positional numeral system that uses twenty symbols: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, A, B, C, D, E, F, G, H, and I, where A represents ten, B eleven, C twelve, D thirteen, E fourteen, F fifteen, G sixteen, H seventeen, and I eighteen, and J nineteen in decimal. Each digit’s position represents a power of 20, starting from $20^0$ at the rightmost digit and increasing to the left. For example, the base-20 number 3J7 equals $3 \times 20^2 + 19 \times 20^1 + 7 \times 20^0 = 1200 + 380 + 7 = 1587$ in decimal. Base-20 has historical significance in some ancient counting systems and is sometimes studied in mathematics to explore alternative numeral systems, positional notation, and arithmetic properties. Understanding base-20 allows learners to perform arithmetic operations, convert numbers between different bases, and analyze patterns in non-decimal systems. While it is rarely used in modern computing or daily life, studying the vigesimal system enhances problem-solving skills, logical reasoning, and comprehension of abstract number representations. It also provides a foundation for higher-level mathematics, coding theory, and theoretical research into efficient ways to represent and manipulate numbers.