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# Write the following in decimal form and say what kind of decimal expansion each has:i) $$\frac{36}{100}$$ ii) $$\frac{1}{11}$$ iii) $$4\frac{1}{8}$$iv)$$\frac{3}{13}$$ v)$$\frac{2}{11}$$ vi)$$\frac{329}{400}$$

i) Clearly, $$\frac{36}{100}$$ can be written as 0.36.
Therefore, it is a terminating decimal.

ii) Dividing 1 by 11, we get$$\require{enclose} \begin{array}{rll} 0.0909 && \hbox{(Explanations)} \\[-3pt] 11 \enclose{longdiv}{100}\kern-.2ex \\[-3pt] \underline{99\phantom{00}} && \hbox{(9 \times 11 = 99)} \\[-3pt] \phantom{0}100 && \hbox{(100 - 99 = 1)} \\[-3pt] \underline{\phantom{0}99} && \hbox{(9 \times 11 = 99)} \\[-3pt] \phantom{00}1 \end{array}$$Hence, $$\frac{1}{11}$$ can be written as 0.090909...
Therefore, it is a non-terminating decimal.

iii) We have, $$4\frac{1}{8}$$ = $$\frac{4×8+1}{8}$$ = $$\frac{33}{8}$$
Dividing 33 by 8, we get, $$\require{enclose} \begin{array}{rll} 4.125 && \hbox{(Explanations)} \\[-3pt] 8 \enclose{longdiv}{33}\kern-.2ex \\[-3pt] \underline{32\phantom{00}} && \hbox{(8 \times 4 = 32)} \\[-3pt] \phantom{0}10 && \hbox{(33 - 32 = 1)} \\[-3pt] \underline{8\phantom{00}} && \hbox{(8 \times 1 = 8)} \\[-3pt] \phantom{0}20 && \hbox{(10 - 8 = 2)} \\[-3pt] \underline{16\phantom{00}} && \hbox{(8 \times 2 = 16)} \\[-3pt] \phantom{0}40 && \hbox{(20 - 16 = 4)} \\[-3pt] \underline{\phantom{0}40} && \hbox{(8 \times 5 = 40)} \\[-3pt] \phantom{00}0 \end{array}$$Hence, $$4\frac{1}{8}$$ can be written as 4.125
Therefore, it is a terminating decimal.

iv) We have, $$\frac{3}{13}$$
Dividing 3 by 13, we get, $$\require{enclose} \begin{array}{rll} 0.230769 && \hbox{(Explanations)} \\[-3pt] 13 \enclose{longdiv}{30}\kern-.2ex \\[-3pt] \underline{26\phantom{00}} && \hbox{(2 \times 13 = 26)} \\[-3pt] \phantom{0}40 && \hbox{(30 - 26 = 4)} \\[-3pt] \underline{39\phantom{00}} && \hbox{(3 \times 13 = 39)} \\[-3pt] \phantom{0}100 && \hbox{(40 - 39 = 1)} \\[-3pt] \underline{91\phantom{00}} && \hbox{(7 \times 13 = 91)} \\[-3pt] \phantom{0}90 && \hbox{(100 - 91 = 4)} \\[-3pt] \underline{78\phantom{00}} && \hbox{(6 \times 13 = 78)} \\[-3pt] \phantom{0}120 && \hbox{(90 - 78 = 12)} \\[-3pt] \underline{\phantom{0}117} && \hbox{(9 \times 13 = 117)} \\[-3pt] \phantom{00}3 \end{array}$$Hence, $$\frac{3}{13}$$ can be written as 0.230769
Therefore, it is a non-terminating decimal.

v) We have, $$\frac{2}{11}$$
Dividing 2 by 11, we get, $$\require{enclose} \begin{array}{rll} 0.1818 && \hbox{(Explanations)} \\[-3pt] 11 \enclose{longdiv}{20}\kern-.2ex \\[-3pt] \underline{11\phantom{00}} && \hbox{(1 \times 11 = 11)} \\[-3pt] \phantom{0}90 && \hbox{(20 - 11 = 9)} \\[-3pt] \underline{88\phantom{00}} && \hbox{(8 \times 11 = 11)} \\[-3pt] \phantom{0}20 && \hbox{(90 - 88 = 2)} \\[-3pt] \underline{11\phantom{00}} && \hbox{(1 \times 11 = 11)} \\[-3pt] \phantom{0}90 && \hbox{(20 - 11 = 9)} \\[-3pt] \underline{\phantom{0}88} && \hbox{(8 \times 11 = 88)} \\[-3pt] \phantom{00}2 \end{array}$$Hence, $$\frac{2}{11}$$ can be written as 0.181818...
Therefore, it is a non-terminating decimal.

vi) We have, $$\frac{329}{400}$$
Dividing 329 by 400, we get, $$\require{enclose} \begin{array}{rll} 0.8225 && \hbox{(Explanations)} \\[-3pt] 400 \enclose{longdiv}{3290}\kern-.2ex \\[-3pt] \underline{3200\phantom{00}} && \hbox{(8 \times 400 = 3200)} \\[-3pt] \phantom{0}900 && \hbox{(3290 - 3200 = 9)} \\[-3pt] \underline{800\phantom{00}} && \hbox{(2 \times 400 = 800)} \\[-3pt] \phantom{0}1000 && \hbox{(900 - 800 = 100)} \\[-3pt] \underline{800\phantom{00}} && \hbox{(2 \times 400 = 800)} \\[-3pt] \phantom{0}2000 && \hbox{(1000 - 800 = 200)} \\[-3pt] \underline{\phantom{0}2000} && \hbox{(5 \times 400 = 400)} \\[-3pt] \phantom{00}0 \end{array}$$Hence, $$\frac{329}{400}$$ can be written as 0.8225
Therefore, it is a terminating decimal.