Question

Find five rational number between
3 and 5

Answer 1

Answer:

31/10

32/10

33/10

40/10

49/10

Step-by-step explanation:

3,5

3=30/10,5=50/10

31/10

32/10

33/10

40/10

49/10

etc .....

Answer 2

Given: Two numbers 3 and 5

To find: Five rational numbers between the given numbers

Solution: To insert rational numbers between 3 and 5, we find the mean of 3 and 5

i.e., $\frac{(3 \ + \ 5)}{2} = \frac{8}{2} = 4$

We find that 3 < 4 < 5.

We now find another rational number between 3 and 4. For this, we need to find mean of 3 and 4.

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

We find that 3 < $\frac{7}{2}$ < 4 < 5

We now find mean of 4 and 5

i.e., $\frac{(4 \ + \ 5)}{2} = \frac{9}{2}$

We find that 3 < $\frac{7}{2}$ < 4 < $\frac{9}{2}$ < 5

Now we find mean of 3 and 7/2

i.e., $\frac{(3 \ + \ \frac{7}{2} )}{2} = \frac{\frac{6 \ + \ 7}{2} }{2} = \frac{13}{4}$

We find that 3 < $\frac{13}{4} < \frac{7}{2}$ < 4 < $\frac{9}{2}$ < 5

We now find mean 4 and $\frac{9}{2}$

i.e., $\frac{(4 \ + \ \frac{9}{2} )}{2} = \frac{\frac{8 \ + \ 9}{2} }{2} = \frac{17}{4}$

We find that $3 < \frac{13}{4} < \frac{7}{2} < 4 < \frac{17}{4} < \frac{9}{2} < 5$

Hence, five rational numbers 3 and 5 are :

$\frac{13}{4}, \frac{7}{2}, 4, \frac{17}{4} \ and \ \frac{9}{2}$