Question

find four rational numbers between 3 and 4.

Answer 1

3.2, 3.4, 3.6 and 3.8.

-WonderGirl

Answer 2

Given: Two numbers 3 and 4

To find: Four rational numbers between the given numbers

Solution: Using mean method:

To insert rational numbers between 3 and 4, we find the mean of 3 and 4

i.e., $\frac{(3 \ + \ 4)}{2} = \frac{7}{2}$

We can see that 3 < $\frac{7}{2}$ < 4

We now find another rational number between $\frac{7}{2}$ and 4. For this, we again find the mean of $\frac{7}{2}$ and 4.

i.e., $\frac{\frac{7}{2} \ + \ 4}{2} = \frac{\frac{7 \ + \ 8}{2} }{2} = \frac{15}{2} * \frac{1}{2} = \frac{15}{4}$

We see that 3 < $\frac{7}{2}$ < $\frac{15}{4}$ < 4

Now we find the mean of $\frac{15}{4}$ and 4.

i.e., $\frac{\frac{15}{4} \ + \ 4}{2} = \frac{\frac{15 \ + \ 16}{4} }{2} = \frac{31}{4} * \frac{1}{2} = \frac{31}{8}$

We see that 3 < $\frac{7}{2} < \frac{15}{4} < \frac{31}{8}$ < 4

Now we find the mean of $\frac{31}{8}$ and 4.

i.e., $\frac{\frac{31}{8} \ + \ 4}{2} = \frac{\frac{31 \ + \ 32}{8} }{2} = \frac{63}{8}* \frac{1}{2} = \frac{63}{16}$

We see that 3 < $\frac{7}{2} < \frac{15}{4} < \frac{31}{8} < \frac{63}{16}$ < 4.

Hence, four rational numbers between 3 and 4 are:

$\frac{7}{2}, \frac{15}{4}, \frac{31}{8} \ and \ \frac{63}{16}$