#### Chapter 1 Number System R.D. Sharma Solutions for Class 9th Math Exercise 1.5

**Exercise 1.5**

1.Â Complete the following sentences:

(i) Every point on the number line corresponds to a .... number which many be either ... or ...

(ii) The decimal form of an irrational number is neither ... nor ...

(iii) The decimal representation of a rational number is either ... or ...

(iv) Every real number is either ... number or ... number.

**Solution**

(iv) Every real number is either rational number or an irrational number because rational or an irrational number is a family of real number.

2. Represent âˆš6, âˆš7 ,âˆš8 on the number line.

We are asked to representÂ âˆš6, âˆš7 ,âˆš8 on the number line

We will follow certain algorithm to represent these numbers on real line

We will consider point A as reference point to measure the distance

3.Â Â Represent âˆš3.5, âˆš9.4 ,âˆš10.5 on the number line .

We are asked to represent the real numbers âˆš3.5 ,Â âˆš9.4 ,Â âˆš10.5 on the real number line

We will follow a certain algorithm to represent these numbers on real number line .

4. Find whether the following statement are true or false.

(i) Every real number is either rational or irrational.

(ii) Ï€ is an irrational number.

(iii) Irrational numbers cannot be represented by points on the number line.

(i) True, because rational or an irrational number is a family of real number. So every real number is either rational or an irrational number.

(ii) True, because the decimal representation of an irrational is always non-terminating or non-repeating. So Ï€ = 3.141..... is an irrational number.

(iii) False, because we can represent irrational numbers by points on the number line.

2. Represent âˆš6, âˆš7 ,âˆš8 on the number line.

**Solution**We are asked to representÂ âˆš6, âˆš7 ,âˆš8 on the number line

We will follow certain algorithm to represent these numbers on real line

We will consider point A as reference point to measure the distance

3.Â Â Represent âˆš3.5, âˆš9.4 ,âˆš10.5 on the number line .

**Solution**We are asked to represent the real numbers âˆš3.5 ,Â âˆš9.4 ,Â âˆš10.5 on the real number line

We will follow a certain algorithm to represent these numbers on real number line .

4. Find whether the following statement are true or false.

(i) Every real number is either rational or irrational.

(ii) Ï€ is an irrational number.

(iii) Irrational numbers cannot be represented by points on the number line.

**Solution**(i) True, because rational or an irrational number is a family of real number. So every real number is either rational or an irrational number.

(ii) True, because the decimal representation of an irrational is always non-terminating or non-repeating. So Ï€ = 3.141..... is an irrational number.

(iii) False, because we can represent irrational numbers by points on the number line.