Question

Choose between which of the two rational numbers does $\pi$ lies ?

• A. $\frac{5}{4}$ and $\frac{13}{3}$
• B. $\frac{3}{8}$ and $\frac{7}{8}$
• C. $\frac{6}{7}$ and $\frac{14}{7}$
• D. None of the above

Answer 1

The correct option is A $\frac{5}{4}$ and $\frac{13}{3}$

$\because \pi =\mathrm{3.14159...}$

Since, $\frac{5}{4}=1.25$ and $\frac{13}{3}=\mathrm{4.333....}$.
So, the irrational number $\mathrm{3.14159....}$ will lie between these two rational numbers.

Since, $\frac{3}{8}=0.375$ and $\frac{7}{8}=0.875$
So, the irrational number $\mathrm{3.14159....}$ will not lie between these two rational numbers.

​​​​​​​Since, $\frac{6}{7}=$$0.\overline{857142}$ and $\frac{14}{7}=2$
So, the irrational number $\mathrm{3.14159....}$ will not lie between these two rational numbers.