Convert Base 6 to Base 9

Convert Base 6 (base 6) to Base 9 (base 9) instantly and accurately.

Selected Base 6 (base 6) - available characters: 0, 1, 2, 3, 4, 5

Conversion Formula

Step-by-step example using the value 42 (decimal):

Convert Base 6 (base 6) → Base 9 (base 9)

Step 1: Expand each digit of 110 (base 6) by position:

        1 × 6^2 = 36
        1 × 6^1 =  6
        0 × 6^0 =  0
        ────────────
        Sum = 42 (decimal)

Step 2: Divide 42 by 9 repeatedly (read remainders upward):

        42 ÷ 9 = 4  r 6
         4 ÷ 9 = 0  r 4
        Read remainders upward: 46

────────────────────────────
Result:  110 (base 6) = 46 (base 9)

About Base 6

Senary (base 6) uses digits 0-5. Each position is a power of 6: 6⁰=1, 6¹=6, 6²=36. Six is divisible by 1, 2, 3, and 6, making fractions clean: 1/2 = 0.3, 1/3 = 0.2 (both terminating). Native to the Ndom language of Papua New Guinea. Standard dice produce one uniform senary digit per roll. Donald Knuth noted senary's compact multiplication table. Conversion: decimal 42 = 1×36+1×6+0 = 110₆.

About Base 9

Nonary (base 9) uses digits 0-8. Each position is a power of 9: 9⁰=1, 9¹=9, 9²=81. Because 9 = 3², each nonary digit maps to exactly 2 ternary digits (0=00 … 8=22). The finite field GF(9) = GF(3²) is used in certain error-correcting codes and algebraic geometry. The 3×3 magic square sums to 15 in every row/column/diagonal and is deeply tied to mod-9 arithmetic. Conversion: decimal 42 = 4×9+6 = 46₉.

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