Class 10 Exam > Class 10 Videos > Real Numbers | Chapter 1 Ex 1.2 Q - Introduction - Theorem 1.2 | NCERT | Maths Class 10th
Real Numbers | Chapter 1 Ex 1.2 Q - Introduction - Theorem 1.2 | NCERT | Maths Class 10th Video Lecture
FAQs on Real Numbers - Chapter 1 Ex 1.2 Q - Introduction - Theorem 1.2 - NCERT - Maths Class 10th Video Lecture
| 1. What are real numbers and why are they important in mathematics? |  |
Ans. Real numbers are a set of numbers that include both rational and irrational numbers. They are important in mathematics because they allow us to represent and work with quantities that can be measured or compared, such as lengths, quantities, and values on a number line.
| 2. What is Theorem 1.2 in Chapter 1 of NCERT Maths Class 10? | |
Ans. Theorem 1.2 states that for any two real numbers a and b, if a < b, then there exists a rational number q such that a < q < b. This theorem shows that between any two real numbers, there is always a rational number.
| 3. How is Theorem 1.2 useful in solving mathematical problems? | |
Ans. Theorem 1.2 is useful in solving mathematical problems as it guarantees the existence of a rational number between any two real numbers. This allows us to estimate or approximate values and helps in solving equations and inequalities involving real numbers.
| 4. Can a real number be both rational and irrational at the same time? | |
Ans. No, a real number cannot be both rational and irrational at the same time. A number is either rational, meaning it can be expressed as a fraction, or it is irrational, meaning it cannot be expressed as a fraction. However, all real numbers can be divided into either rational or irrational numbers.
| 5. How can one determine if a given number is a real number? | |
Ans. Any number that can be expressed as a decimal or a fraction is a real number. This includes whole numbers, integers, rational numbers, and irrational numbers. To determine if a given number is a real number, check if it can be written as a decimal or a fraction.
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