Class 9th, Maths Ch 1 Number System All Important Questions ( That Are Repeated So Many Times In Kvs Exams ) . Is There Any Class 9th Student Or Expert Teacher , Plz Answer My Question .

Mar 8, 2025 by ADMIN 189 views

Class 9th Maths Chapter 1: Number System - All Important Questions

Introduction to Number System

Rational Numbers

Rational numbers are numbers that can be expressed as the ratio of two integers, i.e., in the form of p/q, where p and q are integers and q is not equal to zero. Rational numbers can be expressed in decimal form, and they can be either terminating or recurring decimals. For example, 3/4, 22/7, and 0.5 are all rational numbers.

Irrational Numbers

Irrational numbers are numbers that cannot be expressed as the ratio of two integers. They are non-terminating and non-recurring decimals. For example, √2, π, and e are all irrational numbers.

Real Numbers

Real numbers are all rational and irrational numbers combined. They are all the numbers that can be expressed on the number line, including positive and negative numbers, and zero.

Important Questions in Class 9th Maths Chapter 1

Here are some of the most important questions that are repeated in KVS exams:

1. What is the difference between rational and irrational numbers?

Rational numbers are numbers that can be expressed as the ratio of two integers, while irrational numbers are numbers that cannot be expressed as the ratio of two integers.

2. What is the decimal representation of the rational number 3/4?

The decimal representation of the rational number 3/4 is 0.75.

3. What is the decimal representation of the irrational number √2?

The decimal representation of the irrational number √2 is 1.41421356237... (non-terminating and non-recurring).

4. What is the difference between a rational number and a real number?

A rational number is a type of real number that can be expressed as the ratio of two integers, while a real number is any number that can be expressed on the number line, including rational and irrational numbers.

5. What is the decimal representation of the rational number 22/7?

The decimal representation of the rational number 22/7 is 3.14285714285... (recurring).

6. What is the decimal representation of the irrational number π?

The decimal representation of the irrational number π is 3.14159265359... (non-terminating and non-recurring).

7. What is the difference between a rational number and an irrational number?

A rational number is a number that can be expressed as the ratio of two integers, while an irrational number is a number that cannot be expressed as the ratio of two integers.

8. What is the decimal representation of the rational number 0.5?

The decimal representation of the rational number 0.5 is 0.5 (terminating).

9. What is the decimal representation of the irrational number e?

The decimal representation of the irrational number e is 2.71828182846... (non-terminating and non-recurring).

10. What is the difference between a real number and a complex number?

A real number is any number that can be expressed on the number line, including rational and irrational numbers, while a complex number is a number that can be expressed in the form of a + bi, where a and b are real numbers and i is the imaginary unit.

Conclusion

The number system is a fundamental concept in mathematics that deals with the representation and manipulation of numbers. In Class 9th, students are introduced to the concept of number systems, which is a crucial topic in mathematics. The chapter on number systems in Class 9th is designed to help students understand the basics of numbers, including rational and irrational numbers, real numbers, and complex numbers. The questions mentioned above are some of the most important questions that are repeated in KVS exams, and students should make sure to practice them thoroughly to excel in their exams.

Frequently Asked Questions

Q: What is the difference between a rational number and an irrational number? A: A rational number is a number that can be expressed as the ratio of two integers, while an irrational number is a number that cannot be expressed as the ratio of two integers.
Q: What is the decimal representation of the rational number 3/4? A: The decimal representation of the rational number 3/4 is 0.75.
Q: What is the decimal representation of the irrational number √2? A: The decimal representation of the irrational number √2 is 1.41421356237... (non-terminating and non-recurring).
Q: What is the difference between a rational number and a real number? A: A rational number is a type of real number that can be expressed as the ratio of two integers, while a real number is any number that can be expressed on the number line, including rational and irrational numbers.

Key Takeaways

Rational numbers are numbers that can be expressed as the ratio of two integers.
Irrational numbers are numbers that cannot be expressed as the ratio of two integers.
Real numbers are all rational and irrational numbers combined.
The decimal representation of a rational number is either terminating or recurring, while the decimal representation of an irrational number is non-terminating and non-recurring.
The difference between a rational number and a real number is that a rational number is a type of real number that can be expressed as the ratio of two integers, while a real number is any number that can be expressed on the number line, including rational and irrational numbers.
Class 9th Maths Chapter 1: Number System - Q&A

Q1: What is the difference between a rational number and an irrational number?

A1: A rational number is a number that can be expressed as the ratio of two integers, i.e., in the form of p/q, where p and q are integers and q is not equal to zero. An irrational number is a number that cannot be expressed as the ratio of two integers.

Q2: What is the decimal representation of the rational number 3/4?

A2: The decimal representation of the rational number 3/4 is 0.75.

Q3: What is the decimal representation of the irrational number √2?

A3: The decimal representation of the irrational number √2 is 1.41421356237... (non-terminating and non-recurring).

Q4: What is the difference between a rational number and a real number?

A4: A rational number is a type of real number that can be expressed as the ratio of two integers, while a real number is any number that can be expressed on the number line, including rational and irrational numbers.

Q5: What is the decimal representation of the rational number 22/7?

A5: The decimal representation of the rational number 22/7 is 3.14285714285... (recurring).

Q6: What is the decimal representation of the irrational number π?

A6: The decimal representation of the irrational number π is 3.14159265359... (non-terminating and non-recurring).

Q7: What is the difference between a rational number and an irrational number?

A7: A rational number is a number that can be expressed as the ratio of two integers, while an irrational number is a number that cannot be expressed as the ratio of two integers.

Q8: What is the decimal representation of the rational number 0.5?

A8: The decimal representation of the rational number 0.5 is 0.5 (terminating).

Q9: What is the decimal representation of the irrational number e?

A9: The decimal representation of the irrational number e is 2.71828182846... (non-terminating and non-recurring).

Q10: What is the difference between a real number and a complex number?

A10: A real number is any number that can be expressed on the number line, including rational and irrational numbers, while a complex number is a number that can be expressed in the form of a + bi, where a and b are real numbers and i is the imaginary unit.

Q11: What is the concept of equivalent ratios?

A11: Equivalent ratios are ratios that have the same value, but are expressed in different forms. For example, 2/3 and 4/6 are equivalent ratios.

Q12: What is the concept of like and unlike ratios?

A12: Like ratios are ratios that have the same unit, while unlike ratios are ratios that have different units. For example, 2/3 and 4/5 are like ratios, while 2/3 and 4/6 are unlike ratios.

Q13: What is the concept of greatest common divisor (GCD)?

A13: The greatest common divisor (GCD) of two numbers is the largest number that divides both numbers without leaving a remainder.

Q14: What is the concept of least common multiple (LCM)?

A14: The least common multiple (LCM) of two numbers is the smallest number that is a multiple of both numbers.

Q15: What is the concept of prime factorization?

A15: Prime factorization is the process of expressing a number as a product of its prime factors.

Q16: What is the concept of rationalizing the denominator?

A16: Rationalizing the denominator is the process of removing the radical from the denominator of a fraction.

Q17: What is the concept of simplifying a rational expression?

A17: Simplifying a rational expression is the process of reducing a rational expression to its simplest form.

Q18: What is the concept of adding and subtracting rational expressions?

A18: Adding and subtracting rational expressions involves combining the numerators and denominators of the expressions.

Q19: What is the concept of multiplying and dividing rational expressions?

A19: Multiplying and dividing rational expressions involves multiplying and dividing the numerators and denominators of the expressions.

Q20: What is the concept of simplifying a rational expression with a radical in the denominator?

A20: Simplifying a rational expression with a radical in the denominator involves rationalizing the denominator and then simplifying the expression.

Conclusion

Frequently Asked Questions

Q: What is the difference between a rational number and an irrational number? A: A rational number is a number that can be expressed as the ratio of two integers, while an irrational number is a number that cannot be expressed as the ratio of two integers.
Q: What is the decimal representation of the rational number 3/4? A: The decimal representation of the rational number 3/4 is 0.75.
Q: What is the decimal representation of the irrational number √2? A: The decimal representation of the irrational number √2 is 1.41421356237... (non-terminating and non-recurring).
Q: What is the difference between a rational number and a real number? A: A rational number is a type of real number that can be expressed as the ratio of two integers, while a real number is any number that can be expressed on the number line, including rational and irrational numbers.

Key Takeaways

Rational numbers are numbers that can be expressed as the ratio of two integers.
Irrational numbers are numbers that cannot be expressed as the ratio of two integers.
Real numbers are all rational and irrational numbers combined.
The decimal representation of a rational number is either terminating or recurring, while the decimal representation of an irrational number is non-terminating and non-recurring.
The difference between a rational number and a real number is that a rational number is a type of real number that can be expressed as the ratio of two integers, while a real number is any number that can be expressed on the number line, including rational and irrational numbers.