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

**Exercise 1.5**

1. 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 √6, √7 ,√8 on the number line.

We are asked to represent √6, √7 ,√8 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. Represent √3.5, √9.4 ,√10.5 on the number line .

We are asked to represent the real numbers √3.5 , √9.4 , √10.5 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) π 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 π = 3.141..... is an irrational number.

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

2. Represent √6, √7 ,√8 on the number line.

**Solution**We are asked to represent √6, √7 ,√8 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. Represent √3.5, √9.4 ,√10.5 on the number line .

**Solution**We are asked to represent the real numbers √3.5 , √9.4 , √10.5 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) π 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 π = 3.141..... is an irrational number.

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