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66 SPECIAL TOPICS IN THEORETICAL ARITHMETIC

The most important other fractions exprest in the same
scales.

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3333 5555
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COMPARISON OF RADICES

136. If we examin these tables, we see that the only frac-
tions of this set represented simply in the nonary scale are
1/3 and 2/3. All the other fractions are represented by non-
terminating series of figures. With any odd base the frac-
tions 1/2, 1/4, 1/8, 1/I0 and their proper multiples would
similarly be represented by interminable series.

In the decimal notation these fractions, 1/2, 1/4, 1/8, 1/10
and their proper multiples, are represented by terminating
decimals, but, with the exception of 1/2, not simply. These
most useful fractions are, excepting 1/2, represented very awk-