Revise the Numbers System (Number Play) Chapter for CBSE Class 10 Maths
Looking for Class 10 Maths Numbers System important questions with answers? This practice set from The Busy Brains covers essential concepts from the Numbers System (Number Play) chapter, including the Fundamental Theorem of Arithmetic, Euclid’s Division Algorithm, HCF, LCM, decimal expansions and proofs of irrationality.
The worksheet is divided into four sections according to marks: Section A – 1 mark, Section B – 2 marks, Section C – 3 marks and Section D – 4 marks. It also includes additional practice questions to help students revise important concepts and improve their mathematical reasoning.
Use these CBSE Class 10 Numbers System (Number Play) questions for chapter revision, school tests, pre-board preparation and board exam practice. Attempt each question yourself before watching the video explanation.
Complete Video Solution – Numbers System (Number Play)
Watch the complete video explanation to understand how to solve the questions and present your answers clearly in the examination.
Study tip: Pause the video before each solution and try solving the question independently.
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Class 10 Numbers System (Number Play) Important Questions with Solutions
Prepare for your CBSE Class 10 Maths Board Exam with important questions from Numbers System (Number Play). Practise Euclid’s Division Algorithm, HCF and LCM, prime factorisation, rational and irrational numbers, and terminating decimal expansions.
Section A – 1 Mark Each
Objective questions · 4 × 1 = 4 marks
Q1. State whether the decimal expansion of 13/125 is terminating or non-terminating.
Q2. Write the HCF of two consecutive natural numbers.
Q3. Is the number 0.375 a rational number? Give a reason.
Q4. Write the prime factorisation of 90.
Section B – 2 Marks Each
Short-answer questions · 4 × 2 = 8 marks
Q5. Find the LCM of 24 and 36 using the prime factorisation method.
Q6. Check whether 7/(2³ × 5²) has a terminating decimal expansion or not.
Q7. Find the HCF of 135 and 225 using Euclid’s Division Algorithm.
Q8. Express 17/3123 in decimal form.
Section C – 3 Marks Each
Application-based questions · 2 × 3 = 6 marks
Q9. Use Euclid’s Division Algorithm to find the HCF of 867 and 255.
Q10. Find the largest positive integer that divides 398 and 436, leaving remainders 7 and 11 respectively.
Section D – 4 Marks
Proof-based question · 1 × 4 = 4 marks
Q11. Prove that √5 is irrational.
Quick Revision Tips for Real Numbers
- Practise finding the HCF using Euclid’s Division Algorithm.
- Revise prime factorisation and its application to HCF and LCM.
- Remember the condition for a rational number to have a terminating decimal expansion when written in lowest terms.
- Practise proving that square roots of non-perfect-square natural numbers are irrational.
- Show each step clearly in questions involving algorithms and proofs.
Additional Practice Questions – Real Numbers
Extra questions for independent revision and exam preparation
- Write the decimal expansion of 18 1/8.
- State whether 0.1010010001… is a rational or irrational number.
- Write the HCF of 1 and any prime number.
- Is the number √49 a rational number? Give a reason.
- Find the LCM of 18 and 30 using prime factorisation.
- Check whether the decimal expansion of 19/(2⁴ × 5²) is terminating or non-terminating.
- Express 7/125 in decimal form.
- Use Euclid’s Division Algorithm to find the HCF of 455 and 42.
- Find the largest number that divides 615 and 963, leaving remainder 6 in each case.
- Find the HCF and LCM of 24 and 90 and verify that:
HCF × LCM = Product of the two numbers
- Prove that √3 is irrational.
- Prove that 5 − √2 is irrational.
Why Practise Class 10 Real Numbers Important Questions?
Regular practice helps students strengthen their understanding of rational and irrational numbers, prime factorisation, Euclid’s Division Algorithm and decimal expansions. Working through both short-answer and proof-based questions also helps students organise their solutions and explain mathematical reasoning clearly.
For effective CBSE Class 10 Maths preparation, revise the NCERT chapter, solve the questions independently and review any mistakes before moving to the next topic.
Frequently Asked Questions
1. What are the important topics in Class 10 Real Numbers?
Important topics covered in this practice set include Euclid’s Division Algorithm, HCF and LCM, prime factorisation, decimal expansions of rational numbers, and proofs involving irrational numbers.
2. How do I check whether a rational number has a terminating decimal expansion?
Write the rational number in lowest terms. Its decimal expansion terminates if the denominator has no prime factors other than 2 and 5.
3. How can I prepare for Real Numbers in the CBSE Class 10 Maths exam?
Revise the NCERT chapter, practise HCF and LCM problems, solve decimal-expansion questions and write complete steps for irrationality proofs.
4. Where can I watch the Real Numbers video solution?
Watch the embedded video on this page or visit The Busy Brains YouTube channel.
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