### Theory:

 Natural number Reciprocal Decimal expansion Nature of decimal expansion $$2$$ $$1/2$$ $\frac{1}{2}=0.5$ Terminating decimal expansion $$3$$ $$1/3$$ $\begin{array}{l}\frac{1}{3}=0.33333...\\ =0.\overline{3}\end{array}$ Non-terminating and recurring decimal expansion $$4$$ $$1/4$$ $\frac{1}{4}=0.25$ Terminating decimal expansion $$5$$ $$1/5$$ $\frac{1}{5}=0.2$ Terminating decimal expansion $$6$$ $$1/6$$ $\begin{array}{l}\frac{1}{6}=0.16666...\\ =0.1\overline{6}\end{array}$ Non-terminating and recurring decimal expansion $$7$$ $$1/7$$ $\begin{array}{l}\frac{1}{7}=0.142857142857...\\ =0.\overline{142857}\end{array}$ Non-terminating and recurring decimal expansion $$8$$ $$1/8$$ $\frac{1}{8}=0.125$ Terminating decimal expansion $$9$$ $$1/9$$ $\begin{array}{l}\frac{1}{9}=0.11111...\\ =0.\overline{1}\end{array}$ Non-terminating and recurring decimal expansion $$10$$ $$1/10$$ $\frac{1}{10}=0.1$ Terminating decimal expansion $$11$$ $$1/11$$ $\begin{array}{l}\frac{1}{11}=0.090909...\\ =0.\overline{09}\end{array}$ Non-terminating and recurring decimal expansion $$12$$ $$1/12$$ $\begin{array}{l}\frac{1}{12}=0.083333...\\ =0.08\overline{3}\end{array}$ Non-terminating and recurring decimal expansion $$13$$ $$1/13$$ $\begin{array}{l}\frac{1}{13}=0.076923076923...\\ =0.\overline{076923}\end{array}$ Non-terminating and recurring decimal expansion $$14$$ $$1/14$$ $\begin{array}{l}\frac{1}{14}=0.0714285714285...\\ =0\overline{714285}\end{array}$ Non-terminating and recurring decimal expansion $$15$$ $$1/15$$ $\begin{array}{l}\frac{1}{15}=0.06666...\\ =0\overline{6}\end{array}$ Non-terminating and recurring decimal expansion $$16$$ $$1/16$$ $\frac{1}{16}=0.0625$ Terminating decimal expansion $$17$$ $$1/17$$ $\begin{array}{l}\frac{1}{17}=0.588235294117647...\\ =0.\overline{0588235294117647}\end{array}$ Non-terminating and recurring decimal expansion $$18$$ $$1/18$$ $\begin{array}{l}\frac{1}{18}=0.0555555...\\ =0\overline{5}\end{array}$ Non-terminating and recurring decimal expansion $$19$$ $$1/19$$ $\begin{array}{l}\frac{1}{19}=0.052631578947368421...\\ =0.\overline{052631578947368421}\end{array}$ Non-terminating and recurring decimal expansion $$20$$ $$1/20$$ $\frac{1}{20}=0.05$ Terminating decimal expansion $$21$$ $$1/21$$ $\frac{1}{21}=0.\overline{047619}$ Non-terminating and recurring decimal expansion $$22$$ $$1/22$$ $\frac{1}{22}=0\overline{45}$ Non-terminating and recurring decimal expansion $$23$$ $$1/23$$ $\begin{array}{l}\frac{1}{23}=0.0434782608695652173913...\\ =\overline{0434782608695652173913}\end{array}$ Non-terminating and recurring decimal expansion $$24$$ $$1/24$$ $\begin{array}{l}\frac{1}{24}=0.041666...\\ =0.041\overline{6}\end{array}$ Non-terminating and recurring decimal expansion $$25$$ $$1/25$$ $\frac{1}{25}=0.04$ Terminating decimal expansion