#math/mental Memorize $\dfrac{k}{n}$ for $1 \le k < n < 17$. **$d=6$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{6} & 0.1\overline{6}\\ \tfrac{2}{6} & 0.\overline{3}\\ \tfrac{3}{6} & 0.5\\ \tfrac{4}{6} & 0.\overline{6}\\ \tfrac{5}{6} & 0.8\overline{3}\\ \end{array} $ **$d=7$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{7} & 0.\overline{142857}\\ \tfrac{2}{7} & 0.\overline{285714}\\ \tfrac{3}{7} & 0.\overline{428571}\\ \tfrac{4}{7} & 0.\overline{571428}\\ \tfrac{5}{7} & 0.\overline{714285}\\ \tfrac{6}{7} & 0.\overline{857142}\\ \end{array} $ $ \frac{k}{7}=0.\overline{142857}\ \text{(rotated)};\quad \text{first two digits}=14,28,42,57,71,85 $ **$d=8$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{8} & 0.125\\ \tfrac{2}{8} & 0.25\\ \tfrac{3}{8} & 0.375\\ \tfrac{4}{8} & 0.5\\ \tfrac{5}{8} & 0.625\\ \tfrac{6}{8} & 0.75\\ \tfrac{7}{8} & 0.875\\ \end{array} $ **$d=9$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{9} & 0.\overline{1}\\ \tfrac{2}{9} & 0.\overline{2}\\ \tfrac{3}{9} & 0.\overline{3}\\ \tfrac{4}{9} & 0.\overline{4}\\ \tfrac{5}{9} & 0.\overline{5}\\ \tfrac{6}{9} & 0.\overline{6}\\ \tfrac{7}{9} & 0.\overline{7}\\ \tfrac{8}{9} & 0.\overline{8}\\ \end{array} $ **$d=11$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{11} & 0.\overline{09}\\ \tfrac{2}{11} & 0.\overline{18}\\ \tfrac{3}{11} & 0.\overline{27}\\ \tfrac{4}{11} & 0.\overline{36}\\ \tfrac{5}{11} & 0.\overline{45}\\ \tfrac{6}{11} & 0.\overline{54}\\ \tfrac{7}{11} & 0.\overline{63}\\ \tfrac{8}{11} & 0.\overline{72}\\ \tfrac{9}{11} & 0.\overline{81}\\ \tfrac{10}{11} & 0.\overline{90}\\ \end{array} $ **$d=12$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{12} & 0.08\overline{3}\\ \tfrac{2}{12} & 0.1\overline{6}\\ \tfrac{3}{12} & 0.25\\ \tfrac{4}{12} & 0.\overline{3}\\ \tfrac{5}{12} & 0.41\overline{6}\\ \tfrac{6}{12} & 0.5\\ \tfrac{7}{12} & 0.58\overline{3}\\ \tfrac{8}{12} & 0.\overline{6}\\ \tfrac{9}{12} & 0.75\\ \tfrac{10}{12} & 0.8\overline{3}\\ \tfrac{11}{12} & 0.91\overline{6}\\ \end{array} $ **$d=13$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{13} & 0.\overline{076923}\\ \tfrac{2}{13} & 0.\overline{153846}\\ \tfrac{3}{13} & 0.\overline{230769}\\ \tfrac{4}{13} & 0.\overline{307692}\\ \tfrac{5}{13} & 0.\overline{384615}\\ \tfrac{6}{13} & 0.\overline{461538}\\ \tfrac{7}{13} & 0.\overline{538461}\\ \tfrac{8}{13} & 0.\overline{615384}\\ \tfrac{9}{13} & 0.\overline{692307}\\ \tfrac{10}{13} & 0.\overline{769230}\\ \tfrac{11}{13} & 0.\overline{846153}\\ \tfrac{12}{13} & 0.\overline{923076}\\ \end{array} $ **$d=14$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{14} & 0.0\overline{714285}\\ \tfrac{2}{14} & 0.\overline{142857}\\ \tfrac{3}{14} & 0.2\overline{142857}\\ \tfrac{4}{14} & 0.\overline{285714}\\ \tfrac{5}{14} & 0.3\overline{571428}\\ \tfrac{6}{14} & 0.\overline{428571}\\ \tfrac{7}{14} & 0.5\\ \tfrac{8}{14} & 0.\overline{571428}\\ \tfrac{9}{14} & 0.6\overline{428571}\\ \tfrac{10}{14} & 0.\overline{714285}\\ \tfrac{11}{14} & 0.7\overline{857142}\\ \tfrac{12}{14} & 0.\overline{857142}\\ \tfrac{13}{14} & 0.9\overline{285714}\\ \end{array} $ **$d=15$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{15} & 0.0\overline{6}\\ \tfrac{2}{15} & 0.1\overline{3}\\ \tfrac{3}{15} & 0.2\\ \tfrac{4}{15} & 0.2\overline{6}\\ \tfrac{5}{15} & 0.\overline{3}\\ \tfrac{6}{15} & 0.4\\ \tfrac{7}{15} & 0.4\overline{6}\\ \tfrac{8}{15} & 0.5\overline{3}\\ \tfrac{9}{15} & 0.6\\ \tfrac{10}{15} & 0.\overline{6}\\ \tfrac{11}{15} & 0.7\overline{3}\\ \tfrac{12}{15} & 0.8\\ \tfrac{13}{15} & 0.8\overline{6}\\ \tfrac{14}{15} & 0.9\overline{3}\\ \end{array} $ **$d=16$** $ \begin{array}{r@{\;=\;}l} \tfrac{1}{16} & 0.0625\\ \tfrac{2}{16} & 0.125\\ \tfrac{3}{16} & 0.1875\\ \tfrac{4}{16} & 0.25\\ \tfrac{5}{16} & 0.3125\\ \tfrac{6}{16} & 0.375\\ \tfrac{7}{16} & 0.4375\\ \tfrac{8}{16} & 0.5\\ \tfrac{9}{16} & 0.5625\\ \tfrac{10}{16} & 0.625\\ \tfrac{11}{16} & 0.6875\\ \tfrac{12}{16} & 0.75\\ \tfrac{13}{16} & 0.8125\\ \tfrac{14}{16} & 0.875\\ \tfrac{15}{16} & 0.9375\\ \end{array} $