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Nonary


Nonary is the base-9 numeral system, using the digits 0, 1, 2, 3, 4, 5, 6, 7, and 8. In expanded notation, a nonary numeral d_k...d_0 represents the nonnegative integer

 n=sum_(j=0)^kd_j9^j,

where each d_j is a digit value from 0 to 8. For example, 46_9=4·9+6=42 in decimal. The place values of the fractional part are the negative powers 9^(-1), 9^(-2), ....

The nonary digit strings for successive nonnegative integers, beginning with 0, are 0, 1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, ... (OEIS A007095).

Since 9=3^2, each nonary digit corresponds to two ternary digits, allowing a leading zero within each pair. For example, 46_9=1120_3.


See also

Base, Decimal, Digit, Expanded Notation, Numeral System, Ternary

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References

De Vlieger, M. T. "Multiplication Tables of Various Bases." Updated Nov. 24, 2014. https://dozenal.org/drupal/sites_bck/default/files/MultiplicationSynopsis.pdf.Math Is Fun. "Number Bases." https://www.mathsisfun.com/numbers/bases.html.Sloane, N. J. A. Sequence A007095 in "The On-Line Encyclopedia of Integer Sequences."

Cite this as:

Weisstein, Eric W. "Nonary." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/Nonary.html

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