Question

Four rational numbers between $3$ and $4$ are:

• A. $\frac{3}{5},\frac{4}{5},1,\frac{6}{5}$
• B. $\frac{13}{5},\frac{14}{5},\frac{16}{5},\frac{17}{5}$
• C. $3.1,3.2,4.1,4.2$
• D. $3.1,3.2,3.8,3.9$

Answer 1

The correct option is D $3.1,3.2,3.8,3.9$

To find four rational numbers between $3$ and $4,$ we have to write the given numbers into its equivalent fractions with the same denominators.

$3=\frac{3}{1}=\frac{3\times 5}{1\times 5}=\frac{15}{5}$

and, $4=\frac{4}{1}=\frac{4\times 5}{1\times 5}=\frac{20}{5}$

Between $\frac{15}{5}$ and $\frac{20}{5}$ lies ($\frac{16}{5}=3.2),(\frac{17}{5}=3.4),(\frac{18}{5}=3.6),(\frac{19}{5}=3.8)$

Now, from the given options, in option (a): $1$ is there which is not in between $3$ and $4.$

In option (b), $\frac{13}{5}=2.7,$ which is outside $3$ and $4.$

and, option(c) has $4.1$ and $4.2$ that does not lie between $3$ and $4.$

So, the option (d) is the correct one.