Question

You know that $\frac{1}{7}=0.\overline{142857}$, can you predict what the decimal expression of $\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7}\mathrm{and}\frac{6}{7}$ without actually doing the long division.

Answer 1

Find the Decimal Expansion

It is given that,

$$\begin{gathered} \because \frac{1}{7}=0.\overline{142857} \\ \therefore \frac{2}{7}=2\times \frac{1}{7} \\ =0.\overline{285714} \\ \frac{3}{7}=3\times \frac{1}{7} \\ =0.\overline{428571} \\ \frac{4}{7}=4\times \frac{1}{7} \\ =0.\overline{571428} \\ \frac{5}{7}=5\times \frac{1}{7} \\ =0.\overline{714285} \\ \frac{6}{7}=6\times \frac{1}{7} \\ =0.\overline{857142} \end{gathered}$$