Question

Which of the following is a non-terminating and repeating decimal?

Answer 1

$3\frac{3}{2}+1=\frac{9}{2}+\frac{2}{2}=\frac{11}{2}=5.5,\text{which is a terminating decimal.}$


$2\frac{2}{7}+\frac{6}{7}=\frac{16}{7}+\frac{6}{7}$

$=\frac{22}{7}$

$=\mathrm{3.1428571428...},\text{which is a non-terminating and repeating decimal.}$

$2\frac{5}{7}+\frac{2}{7}=\frac{19}{7}+\frac{2}{7}$

$=\frac{21}{7}$

$=3=3.0,\text{which is a terminating decimal.}$

$2\frac{2}{7}+\frac{1.5}{7}=\frac{16}{7}+\frac{1.5}{7}$

$=\frac{17.5}{7}$

$=2.5,\text{which is a terminating decimal}.$

$\therefore$ Only $2\frac{2}{7}+\frac{6}{7}$ has a non-terminating and repeating decimal expansion.