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Class 10 Maths Chapter 1 Solutions PDF Download

Are you looking for the best and reliable solutions for Class 10 Maths Chapter 1 Real Numbers? If yes, then you have come to the right place. In this article, we will provide you with the links to download the PDF solutions for this chapter from various sources. We will also explain the concepts covered in this chapter and the benefits of using the PDF solutions.

Introduction

The first chapter of the Class 10 Maths syllabus is on real numbers. It is a significant chapter in maths that deals with some of the fundamental topics. This chapter has 6 major parts that need to be covered and understood properly to get a good grasp on real numbers.

What are real numbers?

Real numbers are a combination of rational and irrational numbers. They are the numbers upon which we easily perform mathematical operations. All the numbers which are not imaginary are real numbers. For example, 22, -11, 7.99, 3/2, π (3.14), √2, etc.

Euclid’s division lemma and algorithm

Euclid’s division lemma states that given two integers a and b, there exist unique integers q and r such that a=b×q+r and 0≤r<b. This lemma is used to find the highest common factor (HCF) of two numbers using Euclid's division algorithm. The algorithm is based on repeated application of the lemma until a remainder of zero is obtained. The divisor in that step is the HCF of the given numbers.

Fundamental theorem of arithmetic

The fundamental theorem of arithmetic states that every positive integer greater than 1 can be expressed as a product of prime factors in a unique way. This is also called prime factorisation of a number. For example, 140 = 2 × 2 × 5 × 7 is the prime factorisation of 140. The prime factorisation can be used to find the lowest common multiple (LCM) and HCF of two numbers using the following formula: LCM × HCF = Product of the two numbers.

Decimal expansion of rational and irrational numbers

A rational number is a number that can be expressed as a fraction p/q, where p and q are integers and q ≠ 0. A rational number has either a terminating or a repeating decimal expansion. For example, 1/4 = 0.25 (terminating) and 1/6 = 0.1666… (repeating). An irrational number is a number that cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0. An irrational number has a non-terminating and non-repeating decimal expansion. For example, √2 = 1.414213… and π = 3.141592…

How to download the PDF solutions?

The PDF solutions for Class 10 Maths Chapter 1 Real Numbers are available from various sources online. Some of them are NCERT, Vedantu, and BYJU’S websites. Here are the steps to download the PDF solutions from each of these websites.

Steps to download from NCERT website

1. Go to https://ncert.nic.in/textbook.php?jemh1=0-15
2. Select Class X from the drop-down menu.
3. Select Mathematics from the drop-down menu.
4. Select Chapter-01 from the drop-down menu
5. Click on the PDF icon to download the solutions.

Steps to download from Vedantu website

1. Go to https://www.vedantu.com/ncert-solutions/ncert-solutions-class-10-maths-chapter-1
2. Scroll down to the bottom of the page and click on the Download Free PDF button.
3. Enter your name, email, and phone number to register or log in.
4. Click on the Download Now button to get the solutions.

Steps to download from BYJU’S website

1. Go to https://byjus.com/ncert-solutions-class-10-maths/chapter-1-real-numbers/
2. Scroll down to the end of the page and click on the Download PDF button.
3. Enter your name, email, and phone number to register or log in.
4. Click on the Download Now button to get the solutions.

Benefits of PDF solutions

The PDF solutions for Class 10 Maths Chapter 1 Real Numbers are very helpful for students who want to revise and practice the concepts of this chapter. Here are some of the benefits of using the PDF solutions:

Easy access and offline availability

The PDF solutions can be easily accessed from any device that supports PDF format. You can also save them on your device and use them offline whenever you want. This way, you don’t have to worry about internet connectivity or website issues.

Detailed and step-by-step explanations

The PDF solutions provide detailed and step-by-step explanations for each question and problem in the chapter. They help you understand the logic and method behind each solution. They also help you clear your doubts and avoid mistakes.

Solved examples and exercises

The PDF solutions cover all the solved examples and exercises given in the NCERT textbook. They help you learn from the examples and practice the exercises. They also help you check your answers and improve your accuracy and speed.

Tips and tricks for quick calculations

The PDF solutions also provide some tips and tricks for quick calculations and simplifications. They help you save time and effort while solving the problems. They also help you enhance your mental maths skills and confidence.

Conclusion

In this article, we have provided you with the links to download the PDF solutions for Class 10 Maths Chapter 1 Real Numbers from various sources. We have also explained the concepts covered in this chapter and the benefits of using the PDF solutions. We hope that this article has helped you in your preparation for Class 10 Maths exam. If you have any queries or feedback, please feel free to comment below.

Summary of the main points

• Class 10 Maths Chapter 1 Real Numbers is a significant chapter that deals with some of the fundamental topics in maths.
• The chapter has 6 major parts: what are real numbers, Euclid’s division lemma and algorithm, fundamental theorem of arithmetic, decimal expansion of rational and irrational numbers, etc.
• The PDF solutions for this chapter are available from various sources online such as NCERT, Vedantu, and BYJU’S websites.
• The PDF solutions provide easy access, offline availability, detailed explanations, solved examples, exercises, tips, and tricks for this chapter.

FAQs

1. What is a prime number?

A prime number is a positive integer that has exactly two factors: 1 and itself. For example, 2, 3, 5, 7, 11, etc.

2. What is an irrational number?

An irrational number is a number that cannot be expressed as a fraction p/q, where p and q are integers and q ≠ 0. An irrational number has a non-terminating and non-repeating decimal expansion. For example, √2, π, e, etc.

3. What is a recurring decimal?

A recurring decimal is a decimal that has a repeating pattern of digits after the decimal point. For example, 0.333…, 0.272727…, 0.142857…, etc.

4. What is a co-prime pair?

A co-prime pair is a pair of numbers that have no common factor other than 1. For example, (2, 3), (4, 5), (6, 35), etc.

5. What is a composite number?

A composite number is a positive integer that has more than two factors. For example, 4, 6, 8, 9, 10, etc.

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