jmc

Let's first convert $0.\overline{714285}$ to a fraction. If we define the variable $s$ to be $0.\overline{714285}$, then multiplying both sides of $s=0.\overline{714285}$ by 1,000,000 gives us $$1,000,000s=714,285.\overline{714285}.$$Subtracting $s$ from $1,000,000s$ and $0.\overline{714285}$ from $714,285.\overline{714285}$ tells us that $999,999s=714,285$ and thus $$s=\frac{714,285}{999,999}=\frac{5\cdot 142,857}{7\cdot 142,857}=\frac{5}{7}\cdot \frac{\cancel{142,857}}{\cancel{142,857}}=\frac{5}{7}.$$Note that $714,285=5\cdot 142,857$ and $999,999=7\cdot 142,857$. The reciprocal of $\frac{5}{7}$ is $\frac{7}{5}=\boxed{1.4}.$