Class 9 Exam  >  Class 9 Notes  >  Mathematics (Maths) Class 9  >  Long Question Answers: Number System

Class 9 Maths Chapter 1 Question Answers - Number System

Ques1. Find six rational numbers between 1 and 2.
 
Solution. 

Let x = 1 and y = 2
⇒   y > x
Here n = 6

Class 9 Maths Chapter 1 Question Answers - Number System 
∴ The six rational numbers between 1 and 2 are: (x + d), (x + 2d), (x + 3d), (x + 4d), (x + 5d) and (x + 6d).
Class 9 Maths Chapter 1 Question Answers - Number System

Ques 2. Find five rational numbers between 0.6 and 0.8.
 Solution.
 

Let x = 0.6 and y = 0.8
⇒   y > x
Here, n = 5
∴  Class 9 Maths Chapter 1 Question Answers - Number System
Now, the five rational numbers between 0.6 and 0.8 are: (x + d), (x + 2d), (x + 3d), (x + 4d), and (x + 5d).

Class 9 Maths Chapter 1 Question Answers - Number System

Thus, the required five rational numbers between 0.6 and 0.8 are:  Class 9 Maths Chapter 1 Question Answers - Number System

Ques3. If ‘a’ and ‘b’ are rational numbers and Class 9 Maths Chapter 1 Question Answers - Number System
then find the value of ‘a’ and ‘b’.
Solution.

Class 9 Maths Chapter 1 Question Answers - Number System

Now  Class 9 Maths Chapter 1 Question Answers - Number System
⇒ a + b√8 = 17 +6√8
⇒ a = 17 and b = 6

The document Class 9 Maths Chapter 1 Question Answers - Number System is a part of the Class 9 Course Mathematics (Maths) Class 9.
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FAQs on Class 9 Maths Chapter 1 Question Answers - Number System

1. What is the number system in mathematics?
Ans. The number system in mathematics is a system that represents numbers in a systematic way using symbols or digits. It provides a way to count, measure, and calculate. The most commonly used number system is the decimal system, which uses the digits 0-9.
2. What are the different types of number systems?
Ans. There are several types of number systems, including: - Decimal number system: The decimal system is the most commonly used number system, which uses base 10 and the digits 0-9. - Binary number system: The binary system uses base 2 and consists of only two digits, 0 and 1. It is widely used in computer science and digital electronics. - Octal number system: The octal system uses base 8 and consists of digits 0-7. It is commonly used in computer programming. - Hexadecimal number system: The hexadecimal system uses base 16 and consists of digits 0-9 and letters A-F. It is often used in computer science and coding. - Roman numeral system: The Roman numeral system uses letters to represent numbers. It was used in ancient Rome and is still used in some contexts today.
3. How do you convert numbers between different number systems?
Ans. To convert numbers between different number systems, you can use the following methods: - Decimal to binary: Divide the decimal number by 2 repeatedly, noting the remainders from each division. The binary number is the sequence of remainders in reverse order. - Binary to decimal: Multiply each digit of the binary number by the corresponding power of 2 and add them up. - Decimal to octal: Divide the decimal number by 8 repeatedly, noting the remainders from each division. The octal number is the sequence of remainders in reverse order. - Octal to decimal: Multiply each digit of the octal number by the corresponding power of 8 and add them up. - Decimal to hexadecimal: Divide the decimal number by 16 repeatedly, noting the remainders from each division. Replace remainders greater than 9 with corresponding letters (A-F) in reverse order. - Hexadecimal to decimal: Multiply each digit of the hexadecimal number by the corresponding power of 16 and add them up.
4. What is the importance of the number system in everyday life?
Ans. The number system is important in everyday life for various reasons: - Counting and measuring: The number system allows us to count and measure quantities, such as money, time, distance, and many more. - Mathematics and calculations: The number system forms the foundation of mathematics and allows us to perform calculations, solve equations, and analyze data. - Communication and technology: Number systems are used in various communication systems, such as telephone numbers, IP addresses, and postal codes. They are also essential in technology, including computer programming, digital electronics, and cryptography. - Problem-solving and decision-making: The number system helps in problem-solving and decision-making by providing a logical and organized way to represent and analyze numerical information.
5. How do number systems relate to real-life applications?
Ans. Number systems have numerous real-life applications: - Banking and finance: Number systems are used in banking and finance for calculating interest, managing accounts, and conducting financial transactions. - Engineering and science: Number systems are crucial in engineering and scientific fields, such as physics, chemistry, and electrical engineering, for analyzing data, conducting experiments, and designing systems. - Computer science and technology: Number systems, especially binary and hexadecimal, are fundamental in computer science and technology for representing and processing data in computers, networks, and software. - Medicine and healthcare: Number systems are used in medical measurements, drug dosages, patient monitoring, and medical imaging. - Architecture and construction: Number systems are used in architectural design, construction planning, and measurements for ensuring accuracy and precision in building structures. These are just a few examples of how number systems are applied in various aspects of everyday life.
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