How to find rational numbers between any two numbers for example like finding six rational numbers between three and four please elaborate

The whole series is:

3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4

Step-by-step explanation:

Inserting Numbers Between Two Given Endpoints

Suppose we want to insert n equally-spaced numbers inside a given interval with endpoints [x,y].

To place n numbers, we need to open n+1 slots, at the end of which, a new number will be placed. The given interval is then divided into n+1 rational numbers of a value (y-x)/(n+1) each.

For example, let's add 6 rational numbers between 3 and 4. The width of the given interval is 4-3=1, and we need to place 6 numbers separated by 1/(6+1) = 1/7.

Start by the left endpoint:

3

The first number to add is 3+1/7=22/7

22/7

The second number to add is 22/7+1/7=23/7

23/7

The third number is 23/7+1/7=24/7

24/7

The next numbers follow the same pattern:

25/7

26/7

27/7

The last number is 28/7=4

4

The whole series is:

3, 22/7, 23/7, 24/7, 25/7, 26/7, 27/7, 4

We have inserted 6 rational numbers between 3 and 4.