Class 9 CBSE Mathematics — Chapter 3: The World of Numbers MCQs with Answers
90 practice questions · 30 Easy · 30 Medium · 30 Hard
Practise the most important Class 9 CBSE Mathematics questions from Chapter 3, "The World of Numbers" — 9 separately timed quizzes built from 90 NCERT-aligned multiple-choice questions, with answers and explanations. The set is split into 30 Easy, 30 Medium and 30 Hard, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams and the JEE & NEET foundation years.
"The World of Numbers" is a chapter that rewards problem-solving speed, formula recall and step-by-step reasoning. Each MCQ on this chapter is timed and uses exam-grade marking (+4 correct, −1 wrong, 0 skipped), training the accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on The World of Numbers, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below — answer and worked explanation — and signing in free opens all 90.
Key concepts: The World of Numbers (Class 9 Mathematics)
This chapter completes the number line. Rational numbers are dense but leave gaps; those gaps are filled by irrationals such as √2 and π, and together the two form the real numbers. It also covers converting decimals to fractions, rationalising denominators and the laws of exponents.
- Rational number
- Any number expressible as p/q with p and q integers and q ≠ 0. Every integer qualifies, since n can be written n/1.
- Irrational number
- A number that cannot be written as p/q, such as √2, √3 and π. Its decimal expansion never terminates and never settles into a repeating block.
- Real numbers
- The rationals and irrationals together. Every real number corresponds to exactly one point on the number line, and every point to one real number.
- Density of rationals
- Between any two distinct rational numbers there is another rational — their mean, for instance — so infinitely many rationals lie between any two.
Class 9 Mathematics The World of Numbers MCQs with answers
14 solved questions across the difficulty levels this chapter is graded on — answer and explanation shown for each. The remaining 76 are timed and scored when you sign in.
- Q1Easy
Which of the following is a rational number?
A.√2B.√16✓ CorrectC.√5D.πAnswer: B. √16
Explanation: √16 = 4 because 16 is a perfect square (4×4=16), and 4 = 4/1 is rational. √2, √5 and π have no exact root, so their decimals never terminate or repeat — irrational.
- Q2Easy
The decimal 0.75 written in the form p/q in lowest terms is:
A.3/5B.7/4C.3/4✓ CorrectD.4/3Answer: C. 3/4
Explanation: 0.75 = 75/100 since two decimal places give a denominator of 100; dividing both by their GCD 25 gives 3/4, not 4/3 — don't flip the numerator and denominator.
- Q3Easy
Which of the following is NOT a rational number?
A.0.333…B.√7✓ CorrectC.−5D.22/7Answer: B. √7
Explanation: 7 is not a perfect square, so √7's decimal never terminates or repeats — irrational. 0.333…, −5 and 22/7 can each be written as p/q, so all three are rational.
- Q4Easy
Which fraction is equivalent to 2/3?
A.3/6B.4/9C.2/9D.6/9✓ CorrectAnswer: D. 6/9
Explanation: Multiplying numerator and denominator of 2/3 by 3 gives 6/9 — the same value in a different form. Changing only the numerator or only the denominator, as in 4/9 or 2/9, changes the fraction's value.
- Q5Easy
Every integer is:
A.a rational number✓ CorrectB.not a rational numberC.never a whole numberD.an irrational numberAnswer: A. a rational number
Explanation: Any integer n can be written as n/1, which fits the p/q form with q ≠ 0 — so every integer is rational, never irrational and never excluded from being a whole number.
- Q6Easy
Which of the following lies between 1/4 and 1/2?
A.1/8B.5/8C.3/8✓ CorrectD.3/4Answer: C. 3/8
Explanation: 1/4 = 0.25 and 1/2 = 0.5, and 3/8 = 0.375 sits strictly between them. 1/8 = 0.125 is below 1/4, while 5/8 and 3/4 are both above 1/2.
- Q7Medium
Express 0.454545… (0.45 repeating) as a fraction in lowest terms.
A.45/100B.5/11✓ CorrectC.9/20D.5/9Answer: B. 5/11
Explanation: Let x = 0.4545…; since the repeating block has 2 digits, multiply by 100: 100x = 45.4545…, so 99x = 45 and x = 45/99 = 5/11 in lowest terms.
- Q8Medium
Simplify 3/4 + 5/6 as a fraction in lowest terms.
A.19/12✓ CorrectB.8/10C.15/24D.19/24Answer: A. 19/12
Explanation: The LCM of 4 and 6 is 12, so 3/4 = 9/12 and 5/6 = 10/12; adding gives 19/12. Adding numerators and denominators straight across, as in 8/10, is not how fraction addition works.
- Q9Medium
Which of the following rational numbers lies between −1 and 0?
A.−8/7B.−3/7✓ CorrectC.3/7D.−9/8Answer: B. −3/7
Explanation: −3/7 ≈ −0.43 falls between −1 and 0. −8/7 and −9/8 are both less than −1 in value, and 3/7 is positive, so it lies above 0.
- Q10Medium
The mean of 1/3 and 1/2 is:
A.5/6B.2/5C.5/12✓ CorrectD.1/6Answer: C. 5/12
Explanation: The mean is the sum divided by 2: (1/3 + 1/2) ÷ 2 = (5/6) ÷ 2 = 5/12, not 5/6, which is only the sum of the two fractions before halving.
- Q11Medium
Which of the following lies between 1/5 and 2/5?
A.1/10B.1/2C.3/5D.3/10✓ CorrectAnswer: D. 3/10
Explanation: 1/5 = 0.2 and 2/5 = 0.4, and 3/10 = 0.3 sits strictly between them. 1/10 = 0.1 is below 1/5, while 1/2 and 3/5 are both above 2/5.
- Q12Hard
In proving √2 irrational, we write √2 = p/q in lowest terms. The contradiction reached is that:
A.q must equal 1B.p must be oddC.p and q are both even, contradicting that p/q is in lowest terms✓ CorrectD.p/q is negativeAnswer: C. p and q are both even, contradicting that p/q is in lowest terms
Explanation: From p² = 2q², p must be even; writing p = 2m then forces q² = 2m², so q is even too — both p and q share the factor 2, contradicting that p/q was already in lowest terms.
- Q13Hard
In the proof that √3 is irrational, a key step uses: if 3 divides p², then:
A.3 divides p✓ CorrectB.p is a prime numberC.p² = 3D.3 divides q onlyAnswer: A. 3 divides p
Explanation: Since 3 is prime, if 3 divides p² it must divide p itself — a prime factor of a perfect square is always a factor of the original number, which is what drives the contradiction.
- Q14Hard
Which of the following statements is FALSE?
A.The product of a non-zero rational and an irrational is irrationalB.Between any two rationals there is an irrationalC.The sum of two irrational numbers is always irrational✓ CorrectD.√2 is irrationalAnswer: C. The sum of two irrational numbers is always irrational
Explanation: √2 and −√2 are both irrational, yet √2 + (−√2) = 0, which is rational — so the sum of two irrationals need not be irrational, making that claim false while the other three statements hold.
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Start this chapter free →The World of Numbers — FAQs
What are the key concepts in Class 9 Mathematics The World of Numbers?+
This chapter completes the number line. Rational numbers are dense but leave gaps; those gaps are filled by irrationals such as √2 and π, and together the two form the real numbers. It also covers converting decimals to fractions, rationalising denominators and the laws of exponents. Key ideas include Rational number, Irrational number, Real numbers, Density of rationals.
What does Class 9 Mathematics Chapter 3 (The World of Numbers) cover on XamBaaz?+
It covers 90 NCERT-aligned MCQs on "The World of Numbers" — 30 Easy, 30 Medium and 30 Hard — making 9 separately timed quizzes you can sit without ever repeating the same set, each with an instant explanation, suitable for CBSE Board exams and the JEE & NEET foundation years.
Are these "The World of Numbers" questions free to practise?+
Yes — sign in with Google to practise "The World of Numbers" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "The World of Numbers" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. There are 9 separately timed quizzes on this chapter, so you can come back and get a fresh set rather than re-sitting one you have seen. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Are these "The World of Numbers" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to practise all 90 questions with instant scoring.
Is there negative marking in the "The World of Numbers" quizzes?+
Yes — the timed quizzes use exam-grade marking: +4 for a correct answer, −1 for a wrong one and 0 for a skipped question. Note that MHT-CET and the CBSE board papers themselves carry no negative marking — our mocks for those are scored their way, not this way.
Are these important questions for The World of Numbers?+
The set is curated to the NCERT syllabus and weighted toward the question patterns that actually appear in CBSE Board exams and the JEE & NEET foundation years, across Easy, Medium and Hard — so it doubles as an "important questions" revision list for "The World of Numbers".