🎯 Worksheet Practice
Real Numbers Class 10 Worksheet – Complete Practice Guide
Real Numbers is Chapter 1 of Class 10 Mathematics and provides important foundations for later algebra. This worksheet is designed for repeated practice of the main chapter skills through objective questions, calculations and concept checks. Because questions are generated with changing numerical values, students can practise the same idea without depending on one fixed answer pattern.
1. Euclid's Division Algorithm
For positive integers a and b, division gives a quotient and a remainder. Repeating division with the previous divisor and remainder eventually produces zero. The last non-zero remainder is the HCF.
When solving an HCF problem, write each division step carefully. This reduces calculation mistakes and makes the method easy to verify. The algorithm is especially useful for large integers.
2. Fundamental Theorem of Arithmetic
Every composite number can be written as a product of primes, and this prime factorisation is unique apart from the order of factors. Prime factorisation is central to HCF, LCM and several proof-based questions.
3. HCF and LCM
For two positive integers a and b, the following identity is an important checking tool.
Students should first identify what the question asks and then choose either Euclid's algorithm or prime factorisation. Reduce fractions to lowest terms when a rational-number question requires it.
4. Rational and Irrational Numbers
A rational number can be written as p/q, where p and q are integers and q is not zero. An irrational number cannot be expressed in that form. Familiar examples include √2, √3 and √5. Proof questions involving the square root of a prime commonly use contradiction and divisibility.
5. Decimal Expansions
For a rational number p/q in lowest form, its decimal expansion terminates when the denominator has no prime factors other than 2 and 5. If another prime factor occurs, the decimal expansion is non-terminating recurring.
6. How to Use This Online Worksheet
Select the number of questions, question type, difficulty and optional timer. Press Start New Test. Each question has its own answer box and Check Answer button. The answer remains hidden until the question is checked. Correct answers turn green, incorrect answers turn red, and the progress bar updates automatically.
Shuffle Whole Worksheet generates another set with changing numerical parameters and randomized ordering. Try Easy for concept building, Medium for regular revision and Hard for challenge practice. Sound can be switched off when quiet study is preferred.
7. Exam Preparation Tips
Write Euclidean division steps neatly, verify every prime factor, and check HCF/LCM answers using the product identity. For irrational-number proofs, understand why the assumption leads to a contradiction rather than memorising a paragraph. For decimal questions, always reduce the fraction to lowest terms before examining the denominator.
Use this worksheet for homework, classroom revision, self-study, quick tests and mobile practice. The Print Worksheet button opens the browser print dialog, while Save as PDF uses the same dialog with the PDF destination available on supported devices.