Base 9 Calculator

Formula

To calculate the Base 9 Value (B9):

\[ B9 = \sum (d \times 9^n) \]

Where:

\(B9\) is the base 9 value
\(d\) is the digit in the base 10 number (0-9)
\(n\) is the position of the digit in the base 10 number, starting from 0 on the right

What is Base 9?

Base 9, also known as nonary, is a numeral system that uses nine as its base. It uses digits from 0 to 8. It’s a positional numeral system, meaning the position of a digit in a number determines its value. For example, in the base 9 number 123, the 1 represents 81 (\(9^2\)), the 2 represents 18 (\(9^1\)), and the 3 represents 3 (\(9^0\)).

Example Calculation 1

Let's assume the following value:

Base 10 Number = 123

Using the formula:

\[ B9 = 1 \times 9^2 + 2 \times 9^1 + 3 \times 9^0 = 1 \times 81 + 2 \times 9 + 3 \times 1 = 81 + 18 + 3 = 102 \]

The Base 9 Value is 102.

Example Calculation 2

Let's assume the following value:

Base 10 Number = 456

Using the formula:

\[ B9 = 4 \times 9^2 + 5 \times 9^1 + 6 \times 9^0 = 4 \times 81 + 5 \times 9 + 6 \times 1 = 324 + 45 + 6 = 375 \]

The Base 9 Value is 375.