List five rational numbers between:

(i) − 1 and 0 (ii) − 2 and − 1

(iii) (iv)

Please let us know the method of calculation and logic for that calculation

We know that rational numbers are those numbers which can be written in form where q ≠ 0 or the numbers whose decimal representation in either terminating or repeating after some finite number of steps.

(i) In the given query, the numbers given are –1 and 0.

We have to find the rational numbers between –1 and 0.

Clearly, the numbers are of the form and lies in between –1 and 0.

Hence, the 5 rationals between –1 and 0 are

You can answer the same question in the following way also :

Since you have to find the rationals between –1 and 0.

It is known that –0.1, –0.2, –0.3, –0.4, –0.5, –0.6, –0.7, –0.8, –0.9 etc. all lies in between –1 and 0 and are terminating decimal number.

∴ These numbers are rational numbers. You can give any five out of the above numbers as your answer.

Hence, –0.1, –0.2, –0.3, –0.4, –0.5 are the five rational numbers between –1 and 0.

(iii) The given numbers are

∴ We have to find the 5 rationals between – 0.8 and – 0.4

We can write – 0.8 = – 0.8000 and

– 0.4 = – 0.4000

The rational numbers between – 0.8 and – 0.4 are

These numbers can change as per your choice but the condition is that these numbers must lie in between the numbers – 0.8 and – 0.4 and the decimal representation must be terminating or repeating.

Other parts can be done yourself in the same way. If you face any difficulty then do get back to us.