**Is zero a rational number? can you write it in the form**^{p}/_{q}, where p and q are integers and q≠0. ?

Solution:

Yes, zero is rational number. It can be written as ^{0}/_{1}, ^{0}/_{2} etc., it is in the form of ^{p}/_{q}, where p and q are integers and q≠0

**Find six rational number between 3 and 4**

Solution:

To find six rational numbers between 3 and 4 denominator should be made equal to 6+1 = 7

Therefore, 3 = ^{3×7}/_{7} = ^{21}/_{7} and 4 = ^{4×7}/_{7}

The six rational numbers between 3 and 4 can be found by varying the numerator between 21 and 28 *[because when ^{28}/_{7} = 4 ]*

The numbers are ^{22}/_{7}, ^{23}/_{7}, ^{24}/_{7},^{ 25}/_{7},^{ 26}/_{7},^{ 27}/_{7}.

Solution:

To find five rational numbers between ^{3}/_{5} and ^{4}/_{5}.

Therefore, five rational numbers between ^{3}/_{5} and ^{4}/_{5 }are ** ^{7}/_{10}** ,

**,**

^{3}/_{4}_{ },^{31}/_{40}**,**

^{63}/_{80}

^{127}/_{160}**State whether the following statements are true or false. Give reasons for your answer**

**(i) Every natural number is a whole number**

**(ii)Every integer is a whole number**

**(iii) Every rational number is a whole number**

Solution:

(i)True.

The collection of whole numbers contains all the natural numbers.

(ii) False

Negative numbers are not whole numbers.

(iii)False

Rational numbers are of the form ^{p}/_{q} , where p and q are integers and q ≠ 0. Whole Numbers are simply the numbers **0, 1, 2, 3, 4, 5, …** (and so on).

## 2 thoughts on “Number System – Exercise 1.1 – Class IX”

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