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**NCERT Solutions for Class 10 Maths Chapter 1:** The CBSE Class 10 Maths Chapter deals with Real Numbers. This chapter is crucial both for CBSE Class 10 board exams class 11th. In this chapter, students will learn about Euclid’s Division Lemma, fundamental theorem of Arithmetic, revisiting irrational numbers, revisiting rational numbers and their decimal expressions, etc. The in-text questions given at the end of the chapter will help solidify a student’s understanding of the mathematical concepts.

To help students understand the correct approach to solve different types of questions and provide them with a step-by-step solution, our academic experts have curated the CBSE NCERT Solutions for Class 10 Maths Chapter 1. The Class 10 Maths Solutions are as per the latest CBSE syllabus and help students work on their weak points. Scroll down to download the CBSE NCERT solutions for Class 10 Maths Real Numbers and refer to it at any time.

The exercises and number of questions in the 10th Class Maths chapter 1 are listed below.

Exercise No. | Exercise Topic | No. of Questions |
---|---|---|

Exercise 1.1 | Euclid’s Division Algorithm | 04 |

Exercise 1.2 | Fundamental Theorem of Arithmetic | 07 |

Exercise 1.3 | Irrational Numbers | 03 |

Exercise 1.4 | Rational Numbers and Their Decimal Expansions | 03 |

Students can check the solved exercises for Class 10 Maths Chapter 1 below. They can also **download NCERT Solutions for Real Numbers in PDF** to practice offline*.* The CBSE Class 10 Maths chapter 1 NCERT solutions includes detailed solution for exercises 1.1-1.4.

**Q.1. Use Euclid’s division algorithm to find the HCF of 135 and 225. Solution:** The given numbers are 135 and 225.

Since 225 is greater than 135, we can apply Euclid’s division lemma to a=225 and b=135 to find q and r such that 225=135q+r, 0≤r<135.

So, dividing 225 by 135 we get 1 as the quotient and 90 as remainder i.e. 225=(135×1)+90.

Remainder r is 90 and is not equal to 0, we apply Euclid’s division lemma to a=135 and b=90 to find whole numbers q and r such that 135=90×q+r, 0≤r<90.

So, dividing 135 by 90, we get 1 as the quotient and 45 as remainder i.e. 135=(90×1)+45.

Again, remainder r is 45 and is not equal to 0, so we apply Euclid’s division lemma to a=90 and b=45 to find q and r such that 90=45×q+r, 0≤r<45.

So, dividing 90 by 45, we get 2 as the quotient and 0 as remainder i.e. 90=(2×45)+0.

Since the remainder is 0, the divisor at this stage will be HCF of (135, 225) and the divisor at this stage is 45. Therefore, the HCF of 135 and 225 is 45.

**Q.2. Use Euclid’s division algorithm to find the HCF of 196 and 38220. Solution**: Given numbers, 196 and 38220.

Since 38220 is greater than 196, we can apply Euclid’s division lemma to a=38220 and b=196 to find whole numbers q and r such that 38220=196q+r, 0≤r<196. So, dividing 38220 by 196, we get 195 as the quotient and 0 as remainder r i.e. 38220=(196×195)+0. Because the remainder is zero, divisor at this stage will be HCF. Since divisor at this stage is 196. Therefore, HCF of 196 and 38220 is 196.

Along with Chapter 1, students can avail CBSE NCERT Solutions for Class 10 Maths PDFs for all the remaining chapters. Students should make the best use of the solved examples to score better in the annual exams. Click on the links below to download free, chapter-wise NCERT Solutions for Class 10 Maths.

Real numbers are a coherent part of our lives. Real numbers can be defined as the combination of both rational and irrational numbers. Real numbers can be both positive or negative, and they are denoted by the symbol “R”. Numbers like a natural number, decimals, and fractions come under the real numbers category. Real Numbers are widely used in counting, measuring speed, distance, temperature, time, etc. Even other concepts of Mathematics like Trigonometry, Algebra, Geometry, Probability, Data Handling, etc. make use of real numbers.

Real Number is an important topic in Maths with a weightage of 6 marks. Usually, 3 questions are asked from this chapter on an average.

- One out of three questions in part A (1 mark).
- One out of three questions in part B (2 marks).
- One out of three questions in part C (3 marks).

Embibe’s NCERT Solutions are of great help to the students. Given below are some of the advantages of NCERT solutions by Embibe.

- By following these solutions, students can develop a better understanding of the topics and learn correct problem-solving methods.
- With the help of Embibe’s NCERT solutions, students can solve and revise the entire syllabus of 10th Maths.
- All the exercises from the NCERT 10th Maths textbook have been solved in a detailed and step-wise manner.
- Our academic experts have prepared these solutions according to the latest revised NCERT guidelines.
- Students can also refer to these solutions for revision before the exams.
- Solving problems from NCERT solutions for Class 10 CBSE Maths chapter 1 Real Numbers can also prove beneficial for competitive exams in the future.

**Ans. **The major topics covered in the NCERT Solutions for Class 10 Maths Chapter 1 are Euclid’s division algorithm, revisiting rational & irrational numbers, the fundamental theorem of arithmetic, and decimal expansions.

**Ans. **There are a total of four exercises in the CBSE NCERT solutions for Class 10 Maths.

**Ans. **Yes, the first chapter Real Numbers, is important from an exam perspective and several questions similar to the exercise questions in this chapter will be asked in the final examination. Therefore, these NCERT Class 10 Chapter 1 solutions created by the Embibe’s expert faculty will help students in their exam preparation.

**Ans: **Students can download the NCERT Solutions for Class 10 Maths from this page with the link provided.

**Ans: **There are 41 questions to practice, in the Class 10 Maths Chapter 1 NCERT Solutions.