Question

Which of the following rational numbers does not lie between $\frac{7}{11}$ and $\frac{11}{13}$?

• A. $\overline{0.64}$
• B. $\overline{0.732}$
• C. $\overline{0.637}$
• D. $\overline{0.851}$

Answer 1

The correct option is D $\overline{0.851}$

Consider the rational numbers $\frac{7}{11}$ and $\frac{11}{13}$
$\frac{7}{11}=\mathrm{0.6363...}=\overline{0.63}$
$\frac{11}{13}\approx 0.846$
Since $\overline{0.64}=\mathrm{0.6464...},\frac{7}{11}<\overline{0.64}<\frac{11}{13}$
Now $\overline{0.732}=\mathrm{0.732732...}$
$\therefore \frac{7}{11}<\overline{0.732}<\frac{11}{13}$
Also, $\overline{0.637}=\mathrm{0.637637...}$
$\therefore \frac{7}{11}<\overline{0.637}<\frac{11}{13}$
Last, $\overline{0.851}=\mathrm{0.851851...}$
$\therefore \frac{7}{11}<\frac{11}{13}<\overline{0.851}$
Thus, $\overline{0.851}$ is the rational number that does not lie between $\frac{7}{11}and\frac{11}{13}$
Hence, the correct answer is option (d).