Page:Shinshiki Sanjutsu Kogi 00.djvu/236

六

220

分數に關する整數論的の硏究

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二三の實例は必ずしも蛇足ならじ．

$b=3$ 又は $b=9$，$10\equiv 1{\pmod {3}}{\pmod {9}}\quad c=1$

${\begin{aligned}{\frac {1}{3}}&=0.333\cdots \qquad {\frac {2}{3}}=0.666\cdots \\{\frac {1}{9}}&=0.111\cdots \quad {\frac {2}{9}}=0.222\cdots \quad {\frac {4}{9}}=0.444\cdots ,\quad \cdots \end{aligned}}$

$b=11$，$10^{2}-1=99=9\times 11.\quad c=2$

${\begin{aligned}{\frac {1}{11}}&=0.{\overline {09}}\qquad {\frac {10}{11}}=0.{\overline {90}}\\{\frac {2}{11}}&=0.{\overline {18}}\qquad {\frac {9}{11}}=0.{\overline {81}}\\{\frac {3}{11}}&=0.{\overline {27}}\qquad {\frac {8}{11}}=0.{\overline {72}}\\{\frac {4}{11}}&=0.{\overline {36}}\qquad {\frac {7}{11}}=0.{\overline {63}}\\{\frac {5}{11}}&=0.{\overline {45}}\qquad {\frac {6}{11}}=0.{\overline {54}}\end{aligned}}$