NCERT Solutions for Class 9 Maths Chapter 1 Number Systems (Ex 1.5) Exercise 1.5

NCERT Solutions for Class 9 Chapter 1 Number Systems -Free PDF Download

NCERT Solutions for Class 9 Maths Chapter 1 are about the numbers. There are various types of numbers that have different properties. In this chapter, students will understand how to solve questions on various types of numbers. In Class 9 Maths Chapter 1 Exercise 1.5, you will face problems related to rational and irrational numbers. We, at CoolGyan, give you a complete solution to Class 9 Maths Chapter 1 Exercise 1.5.

Maths Revision Notes for Class 9

CBSE Class 9 Mathematics
NCERT Solutions
CHAPTER 1
Number Systems(Ex. 1.5)

. Classify the following numbers as rational or irrational:

(i) 
(ii) 
(iii) 
(iv) 
(v) 

Solutions:- (i) 
We know that


which is also an irrational number.
Therefore, we conclude thatis an irrational number.

(ii) 

= 3
Therefore, we conclude thatis a rational number.

(iii) 
We can cancelin the numerator and denominator, asis the common number in numerator as well as denominator, to get

Therefore, we conclude thatis a rational number.

(iv) 
We know that.
We can conclude that, when 1 is divided by, we will get an irrational number.
Therefore, we conclude thatis an irrational number.

(v) 
We know that
We can conclude that  will also be an irrational number.
Therefore, we conclude that  is an irrational number.

2. Simplify each of the following expressions:
(i) 
(ii) 
(iii) 
(iv)
Ans. (i) 
We need to apply distributive law to find value of.


Therefore, on simplifying, we get.

(ii) 
We need to apply distributive law to find value of.

Therefore, on simplifying, we get 6.

(iii) 
We need to apply the formula to find value of.

Therefore, on simplifying, we get.

(iv) 
We need to apply the formula to find value of.

= 5-2 = 3
Therefore, on simplifying, we get 3.

3. Recall, is defined as the ratio of the circumference (say c) of a circle to its diameter (say d). That is,. This seems to contradict the fact that is irrational. How will you resolve this contradiction?

Ans. We know that when we measure the length of a line or a figure by using a scale or any device, we do not get an exact measurement. In fact, we get an approximate rational value. So, we are not able to realize that either circumference (c) or diameter(d) of a circle is irrational.

Therefore, we can conclude that as such there is not any contradiction regarding the value of and we realize that the value of  is irrational.

4. Represent 9.3 on the number line.

Ans. Mark the distance 9.3 units from a fixed point A on a given line to obtain a point B such that AB = 9.3 units. From B mark a distance of 1 unit and call the new point as C. Find the mid-point of AC and call that point as O. Draw a semi-circle with centre O and radius OC = 5.15 units. Draw a line perpendicular to AC passing through B cutting the semi-circle at D.
Then BD =BE= where point B is zero point of number line.

5. Rationalize the denominators of the following:

(i) 

(ii)

(iii)

(iv)

Ans. (i) 
We need to multiply the numerator and denominator ofby, to get
.
Therefore, we conclude that on rationalizing the denominator of, we get.

(ii) 
We need to multiply the numerator and denominator ofby, to get
.
We need to apply the formulain the denominator to get



Therefore, we conclude that on rationalizing the denominator of, we get.

(iii) 
We need to multiply the numerator and denominator ofby, to get
.
We need to apply the formulain the denominator to get



Therefore, we conclude that on rationalizing the denominator of, we get.

(iv) 
We need to multiply the numerator and denominator ofby, to get
.
We need to apply the formulain the denominator to get



Therefore, we conclude that on rationalizing the denominator of, we get.