Question

Write 5 rational between two consecutive rational numbers

Answer 1

Let's say the 2 numbers 3.5 and 3.6 are consecutive rational numbers then no rational number should come in between them but what about 3.55 in fact there can always be a ratinal number between any 2 rational numbers, no matter how close they are. The only way to define consecutive here would be consecutive rational numbers in fixed decimal places. So if we consider rational numbers to a fixed decimal place e.g. Upto 1 decimal place could be 3.4, 3.5, 3.6. Upto 2 decimal place could be 2.94, 2.95, 2.96

2nd problem and the bigger one.

Where does an irrational number exactly lie on a number line e.g sqrt(2), pi. There is no way to find their exact value in decimal and hence they are called irrational. The technique of defining fixed decimal places won't work here cause the moment you round of an irrational no to some fixed decimal places, the number no longer remains irrational, it becomes a rational no.

Hope this helps.