Converting Decimals

Converting a decimal from base-n to a base-10 fraction involves a similar expansion process as with integers, but with negative powers of the base.

For example, to convert $.321_6$ to a base-10 fraction:

$.321_6 = 3 \times 6^{-1} + 2 \times 6^{-2} + 1 \times 6^{-3} = \frac{3}{6} + \frac{2}{36} + \frac{1}{216} = \frac{108 + 12 + 1}{216} = \frac{121}{216}$.

Converting from a base-10 decimal to a base-n decimal is rarely tested due to its complexity. Problems usually ask for a reduced base-10 fraction as the answer.