We know that there are infinite rational numbers between any two numbers.

A rational number is the one that can be written in the form of p/q, where p and q are integers and q ≠ 0.

We know that the numbers 3/5 and 4/5 can also be written as 0.6 and 0.8 .

We can conclude that the numbers 0.61, 0.62, 0.63, 0.64 and 0.65 all lie between 0.6 and 0.8

We need to rewrite the numbers 0.61, 0.62, 0.63, 0.64 and 0.65 in p/q form to get the rational numbers between 3 and 4.

So, after converting, we get 61/100,62/100,63/100,64/100 and 65/100.

We can further convert the rational numbers 62/100,64/100 and 65/10 into lowest fractions.

On converting the fractions, we get 31/50,16/25 and 13/20.

Therefore, six rational numbers between 3 and 4 are 61/100,31/50,63/100,16/25 and 13/50.