Important Questions – Chapter 1: Real Numbers (Class 9 PCTB)

The following questions are based on the Punjab Curriculum and Textbook Board (PCTB) syllabus and cover the most important concepts that frequently appear in school examinations.

Short Questions

Define a Rational Number.
Define an Irrational Number.
What are Real Numbers?
Differentiate between terminating and recurring decimals.
State the Reflexive Property of Equality.
State the Symmetric Property of Equality.
State the Transitive Property of Equality.
How can you determine whether a number is rational or irrational?
What is a surd?
What is a conjugate surd?

Conceptual Questions

Classify the following numbers as Rational or Irrational:

(i)	√2
(ii)	√9
(iii)	π
(iii)	0.75
(iv)	0.333…
(v)	2.121221222…

2. Explain why every rational number is a real number.

3. Give three examples each of rational and irrational numbers.

4. Explain the importance of real numbers in mathematics.

Number Line Questions

Represent √2 on the number line.
Represent √3 on the number line.
Represent √5 on the number line.
Locate the following numbers on the number line:
- 1.5
- −2
- 3/4

Exercise-Based Numerical Questions

Rational Numbers

Write the following decimals in the form p/q:
- 0.25
- 0.125
- 0.75
Find two rational numbers between:
- 1 and 2
- 3/5 and 4/5
- 7/8 and 1

Surds and Radicals

Simplify:
- √75
- √108
- √200
Simplify:
- √75 + √27
- 3√8 − √18
- 2√50 + 3√8
Multiply:
- √3 × √12
- (2 + √5)(2 − √5)

Rationalization

Rationalize the denominator:
- 1/√2
- 3/√5
- 5/√7
Rationalize:
- 1/(2 + √3)
- 3/(5 − √2)
- 4/(√7 + √5)

Long Questions

Question No.1:

Question No.2:

Question No.3:

Question No.4:

Question No.5:

Question No.6:

Important Review Exercise Questions

Students should pay special attention to:

Classification of numbers
Properties of equality
Representation of irrational numbers on the number line
Simplification of surds
Rationalization of denominators
Operations involving surds and conjugates

Most Important Exam Questions

If a student has limited time, these are the highest-priority questions:

Prove that √2 is irrational.
Represent √5 on the number line.
Rationalize 1/(2 + √3).
Simplify √75 + √27.
Find two rational numbers between 3/5 and 4/5.
Distinguish between rational and irrational numbers.
State and apply the properties of equality.
Simplify expressions involving surds and conjugates.

You May be Interested In: