By actual division, express each of the following as a repeating decimal :

(i) $\dfrac{103}{9}$

(ii) $\dfrac{7}{12}$

(iii) $\dfrac{101}{15}$

(iv) $\dfrac{303}{11}$

(v) $\dfrac{212}{143}$

(vi) $\dfrac{16}{7}$

(vii) $\dfrac{227}{30}$

(viii) $\dfrac{2000}{33}$

(i) $\dfrac{103}{9}$

By actual division, we have:

$\begin{array}{r} 11.444… \ 9 \overline{) 103.000} \ \underline{-9\phantom{.000}} \ 13\phantom{.000} \ \underline{-9\phantom{.000}} \ 4.0\phantom{00} \ \underline{-3.6\phantom{00}} \ 40\phantom{0} \ \underline{-36\phantom{0}} \ 40 \ \underline{-36} \ 4… \end{array}$

∴ $\dfrac{103}{9} = 11.444… = 11.\overline{4}$

(ii) $\dfrac{7}{12}$

By actual division, we have:

$\begin{array}{r} 0.5833… \ 12 \overline{) 7.0000} \ \underline{-0\phantom{.0000}} \ 70\phantom{000} \ \underline{-60\phantom{000}} \ 100\phantom{00} \ \underline{-96\phantom{00}} \ 40\phantom{0} \ \underline{-36\phantom{0}} \ 40 \ \underline{-36} \ 4… \end{array}$

∴ $\dfrac{7}{12} = 0.5833… = 0.58\overline{3}$

(iii) $\dfrac{101}{15}$

By actual division, we have:

$\begin{array}{r} 6.733… \ 15 \overline{) 101.000} \ \underline{-90\phantom{.000}} \ 110\phantom{00} \ \underline{-105\phantom{00}} \ 50\phantom{0} \ \underline{-45\phantom{0}} \ 50 \ \underline{-45} \ 5… \end{array}$

∴ $\dfrac{101}{15} = 6.733… = 6.7\overline{3}$

(iv) $\dfrac{303}{11}$

By actual division, we have:

$\begin{array}{r} 27.5454… \ 11 \overline{) 303.0000} \ \underline{-22\phantom{.0000}} \ 83\phantom{.0000} \ \underline{-77\phantom{.0000}} \ 60\phantom{000} \ \underline{-55\phantom{000}} \ 50\phantom{00} \ \underline{-44\phantom{00}} \ 60\phantom{0} \ \underline{-55\phantom{0}} \ 50 \ \underline{-44} \ 6… \end{array}$

∴ $\dfrac{303}{11} = 27.5454… = 27.\overline{54}$

(v) $\dfrac{212}{143}$

By actual division, we have:

$\begin{array}{r} 1.482517… \ 143 \overline{) 212.000000} \ \underline{-143\phantom{.000000}} \ 690\phantom{00000} \ \underline{-572\phantom{00000}} \ 1180\phantom{0000} \ \underline{-1144\phantom{0000}} \ 360\phantom{000} \ \underline{-286\phantom{000}} \ 740\phantom{00} \ \underline{-715\phantom{00}} \ 250\phantom{0} \ \underline{-143\phantom{0}} \ 1070 \ \underline{-1001} \ 69… \end{array}$

∴ $\dfrac{212}{143} = 1.482517482517… = 1.\overline{482517}$

(vi) $\dfrac{16}{7}$

By actual division, we have:

$\begin{array}{r} 2.285714… \ 7 \overline{) 16.000000} \ \underline{-14\phantom{.000000}} \ 20\phantom{00000} \ \underline{-14\phantom{00000}} \ 60\phantom{0000} \ \underline{-56\phantom{0000}} \ 40\phantom{000} \ \underline{-35\phantom{000}} \ 50\phantom{00} \ \underline{-49\phantom{00}} \ 10\phantom{0} \ \underline{-7\phantom{0}} \ 30 \ \underline{-28} \ 2… \end{array}$

∴ $\dfrac{16}{7} = 2.285714… = 2.\overline{285714}$

(vii) $\dfrac{227}{30}$

By actual division, we have:

$\begin{array}{r} 7.566… \ 30 \overline{) 227.000} \ \underline{-210\phantom{.000}} \ 170\phantom{00} \ \underline{-150\phantom{00}} \ 200\phantom{0} \ \underline{-180\phantom{0}} \ 200 \ \underline{-180} \ 20… \end{array}$

∴ $\dfrac{227}{30} = 7.566… = 7.5\overline{6}$

(viii) $\dfrac{2000}{33}$

By actual division, we have:

$\begin{array}{r} 60.6060… \ 33 \overline{) 2000.0000} \ \underline{-198\phantom{0.0000}} \ 20\phantom{.0000} \ \underline{-0\phantom{.0000}} \ 200\phantom{000} \ \underline{-198\phantom{000}} \ 20\phantom{00} \ \underline{-0\phantom{00}} \ 200\phantom{0} \ \underline{-198\phantom{0}} \ 20 \ \underline{-0} \ 20… \end{array}$

∴ $\dfrac{2000}{33} = 60.6060… = 60.\overline{60}$