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**Q.1Â Â Â Â Is zero a rational number ? Can you write it in the form , where p and q are integers and **

**Sol.**

Yes, zero is a rational number.Â

Zero can be written in any of the following forms :Â

and so on.

Thus, 0 can be written as , where p = 0 and q is any non- zero integer.

Hence , 0 is a rational number.

Â **Q.2Â Â Â Â Â Find six rational numbers between 3 and 4.**

**Sol. **

We know that between two rational numbers x and y, such that x < y, there is a rational number . That is ,

There are two rational numbers 3 and 4 , such that 3 < 4 , a rational number between 3 and 4 is

Therefore

Now ,two rational numbers 3 and such that, a rational number between 3 and

There are two rational numbers and 4 , a rational number between and 4 is

Therefore

There are two rational numbers 3 and Â ,a rational number between 3 and

There are two rational numbers and 4 , a rational number between and 4 is

There are two rational numbers and 4 , a rational number between and 4 is

Therefore

Hence, six rational numbers between 3 and 4 are :

**ALTERNATIVE METHOD**

Since we want 6 rational number between 3 and 4, so we write

We know that 21 < 22 < 23 < 24 < 25 < 26 < 27 < 28

Â

Hence, six rational numbers between

**Q.3Â Â Â Â Â Find five rational numbers between . **

**Sol. **

Since we want 5 rational numbers between , so we write.

and

We know that 18 < 19 < 20 < 21 < 22 < 23 < 24

Â Â

Hence , 5 rational numbers between

**Q.4Â Â Â Â State whether the following statements are true or false. Give reasons for your answers.Â Â Â Â Â Â Â Â Â Â **

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

Â Â Â Â Â Â Â Â Â Â Â Â Â Â Â

*(i) True : Every natural number lies in the collection of whole numbers. *

(ii) False : -3 is not a whole number.

(iii) False is not a whole number.

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