Question

You know that $\frac{1}{7}=0.142857$. Find the decimal expansions of $\frac{2}{7},\frac{3}{7},\frac{4}{7},\frac{5}{7},\frac{6}{7}$ are without actually doing the long division?

Answer 1

It is given that $\frac{1}{7}=0.142857$.

Now,

$\frac{2}{7}=2\times \frac{1}{7}$

$=2\times 0.142857$

$=0.285714$

$\frac{3}{7}=3\times \frac{1}{7}$

$=3\times 0.142857$

$=0.428571$

$\frac{4}{7}=4\times \frac{1}{7}$

$=4\times 0.142857$

$=0.571428$

$\frac{5}{7}=5\times \frac{1}{7}$

$=5\times 0.142857$

$=0.714285$

$\frac{6}{7}=6\times \frac{1}{7}$

$=6\times 0.142857$

$=0.857142$