NCERT Solutions for Class 9 Maths Chapter 1 Exercise 1.2

Vishal kumarUpdated on 15 May 2025, 02:38 PM IST

Through irrational numbers the number system extends into space occupied by values that cannot be classified as fractional numbers. The numeric representations √2 and π both possess extended decimal sequences that never end and never repeat digits. The understanding of different real numbers in the number line becomes clearer through visual representation of their placement. The fundamental number concepts prepared us to tackle additional topics involving roots and exponents together with equations.

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NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems Exercise 1.2
Access Solution of Number Systems Class 9 Chapter 1 Exercise: 1.2
Topics covered in Chapter 1 Number System: Exercise 1.2
Also see-
NCERT Solutions of Class 9 Subject Wise
NCERT Exemplar Solutions of Class 9 Subject Wise

exercise1.2

Students who use NCERT Solutions and NCERT Books have a proven method to prepare for irrational numbers and their properties along with operations. The resources simplify challenging concepts by providing solved illustrations and exercise structures which lead to easy subject comprehension. Students derive advantages from each step explained explanations because they strengthen fundamental concepts and improve understanding. Students who refer to these established learning materials will develop their analytical capabilities.

NCERT Solutions for Class 9 Maths Chapter 1 – Number Systems Exercise 1.2

Access Solution of Number Systems Class 9 Chapter 1 Exercise: 1.2

Q1 (i) State whether the following statements are true or false. Justify your answers. (i) Every irrational number is a real number.

Answer:

(i) True
The set of real numbers includes both rational and irrational numbers.

Q1 (ii) State whether the following statements are true or false. Justify your answers. (ii) Every point on the number line is of the form $\sqrt{m}$ , where m is a natural number.

Answer:

(ii) False

Many points on the number line are rational (like 2, $\frac{1}{2}$, etc.) which are not in the form $\sqrt{m}$.

Q1 (iii) State whether the following statements are true or false. Justify your answers. (iii) Every real number is an irrational number.

Answer:

(iii) False

Real numbers include both rational and irrational numbers. For example, 3 is a real number but not irrational.

Q2 Are the square roots of all positive integers irrational? If not, give an example of the square root of a number that is a rational number.

Answer:

No, the square roots of all positive integers are not irrational.

Example:

$\sqrt{4}$ = 2, which is a rational number.

Q3 Show how $\sqrt{5}$ can be represented on the number line.

Answer:

Construction method (simplified):

We know that

$\sqrt{5} = \sqrt{(2)^2+(1)^2}$

Now,

Let OA be a line on the number line that is 2 units long. Next, link OB and build AB of unit length perpendicular to OA.

Now, in right angle triangle OAB, by Pythagoras theorem

OB = $\sqrt{(2)^2+(1)^2}=\sqrt{5}$

Now, draw an arc that intersects the number line at C using O as the center and OB as the radius.

Point C represent $\sqrt{5}$ on a number line.

Also Read:

Topics covered in Chapter 1 Number System: Exercise 1.2

Concept of irrational numbers: Numbers classified as irrational cannot be expressed as fractions with integer values p and q. Numerical forms of irrational numbers hold infinite decimal expansions without repeating patterns.
Difference between rational and irrational numbers: Any number expressed as a fraction will always represent a rational number while producing a terminating or repeating decimal result. Irrational numbers resist fraction representation and expand into endless sequences of digits without repeating patterns.
Properties of irrational numbers: Real numbers include irrationals which cannot be completed as decimal expansions. The combination of a rational number together with an irrational number usually produces an irrational outcome unless one is zero when multiplying.
Representation of irrational numbers on the number line: One can place irrational numbers on the number line through geometrically based methods. People can identify points through right triangle construction followed by a ruler and compass technique.
Use of Pythagoras theorem to construct irrational numbers: Using the Pythagoras theorem enables creation of irrational numbers. The hypotenuse in a right-angled triangle having legs of 1 unit measures the irrational value of $\sqrt{2}$.

Also see-

NCERT Solutions of Class 9 Subject Wise

Students must check the NCERT solutions for class 9 of Mathematics and Science Subjects.

NCERT Exemplar Solutions of Class 9 Subject Wise

Students must check the NCERT Exemplar solutions for class 9 of Mathematics and Science Subjects.

Frequently Asked Questions (FAQs)

Q: According to NCERT solutions for Class 9 Maths chapter 1 exercise 1.2 , How are real numbers classified?

Real numbers are the union of both rational and irrational numbers.

Q: 1/3 is a ______ number

Thus 1/3 is a rational number.

Q: Say true /false: On a number line, a number on the left is always greater than a number on the right.

The given statement is false. A number on the left is always less than a number on the right because the left side of zero was occupied by the negative numbers on the number line.

Q: A number on the right is always _______ than a number on the left.

A number on the right is always greater than a number on the left. Since all positive numbers occupy the right side of the zero.

Q: How many numbers can be represented in a number line?

Mathematically, number lines extend indefinitely at both ends. So an infinite number can be represented in a number line.

Q: Integers are a subset of _______

Integers are a subset of rational numbers.

Q: Say true or false: Rational Numbers are a subset of Real Numbers.

Yes, the given statement is true. Rational Numbers and irrational numbers are a subset of Real Numbers. Real numbers are the union of both rational and irrational numbers.

Q: What is a number line?

The horizontal straight lines in which the integers are placed in equal intervals are known as number lines.

Q: ___ is the middle point of the number line.

0 is the middle point of the number line.

Q: In the NCERT solutions for Class 9 Maths chapter 1 exercise 1.2 , how many questions and what types of questions are there?

NCERT solutions for Class 9 Maths chapter 1 exercise 1.2 consists of 4 questions and the questions are based on the concept of rational and irrational numbers, differences regarding rational and irrational numbers and how to identify them, and also how to locate them on a number line.

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