A) \[8.\overset{\bullet }{\mathop{9}}\,\overset{\bullet }{\mathop{1}}\,\overset{\bullet }{\mathop{2}}\,\]
B) \[8.9\overset{\bullet }{\mathop{1}}\,\overset{\bullet }{\mathop{2}}\,\]
C) \[8.97\overset{\bullet }{\mathop{9}}\,\]
D) \[8.9\overset{\bullet }{\mathop{7}}\,\overset{\bullet }{\mathop{9}}\,\]
Correct Answer: C
Solution :
\[8.3\overset{\bullet }{\mathop{1}}\,=8\frac{31-3}{90}=8\frac{28}{90}=\frac{748}{90}\] \[0.\overset{\bullet }{\mathop{6}}\,=\frac{6}{9}\] \[0.00\overset{\bullet }{\mathop{2}}\,=\frac{2}{900}\] \[\therefore \] \[=8.3\overset{\bullet }{\mathop{1}}\,+0.\overset{\bullet }{\mathop{6}}\,=0.00\overset{\bullet }{\mathop{2}}\,=\frac{748}{90}+\frac{6}{9}+\frac{2}{900}\] \[=\frac{7480+600+2}{900}=\frac{8082}{900}=8.97\overset{\bullet }{\mathop{9}}\,\]
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